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## Fighting of the Cause of Allah by Governing a Smart Mathematics Based on Islamic Teology

Existence of the universe is reality evidence of supremacy and science fame of God Allah SWT. Inking seven of times water in all ocean world (even more) not enough to write down it. According to writer, mathematical model which representatively as stepping in developing the Islamic Scientific is arctangent differential equation

Eqs.(1)

which its exact solution is of the form:

Eqs.(2)

Because of writer looks into this arctangent differential equation is having the religion character
(according to writer that for a=1, b=1, and both of initial values t0 = 0 dan y0 = 0 the value of the tangent function at correspond to the Qidam and Baqa properties), hence solution yielded a solver technique entering religion factors must still appropriate to the exact solution

This paper introduces a new technique of solving a nonlinear first order ordinary differential equation so-called as SMT (stands for Stable Modulation Technique) which its solution is in the form of AF(A), that is a formula of modulation function which its amplitude term is also including in the phase function. The transfromation function applied for solving eq.(1) by using SMT is what gives its final solution in the form :

Eqs.(3)

The idea of developing this stable modulation technique based on the event of Isra’ and Mi’raj of prophet Muhammad, which alongside its journey towards Sidhratulmuntaha guided by angel Jibril. Eqs.(3) assures writer that when mi’raj the energy of prophet Muhammad is transferred into the energy form of modulated wave. The fundamental aspect for developing of modern mathematics and computing is obtained when to = 0, yo = 0, a = 0 dan b = 0 where eq.(3) then reduces to the form :

Eqs .(4)

Eqs.(4) as a representative form of tangent function up to now has not been met in Mathematics Handbook, because the only

Eqs .(5)

But both of eq.(4) and eq.(5) are still giving the same value with the value of tan(t) for all values of t except at t = pi / 2 in eq.(4) and at t = pi in eq.(5) which both giving value of 0/0, though value of tan(pi/2) = ~. In mathematics the value of 0/0 is unknown as commonly called as NaN (stands for Not a Number). The value of ~ is still not obtaining from eq.(4) and eq.(5), even if has been performed the limit operation because it is only giving devide by zero:

Eqs .(6)

At presentation of the exact solution of arctangent differential equation brightens the confidence of writer that during journey Isra’, angel Jibril telling the exact properties of God, while during journey Mi’raj of prophet Muhammad is supplied by a stabilization of believe that God doesn’t spell out members as apparently at 0/0, and man will never can reach God will desire, as apparently at 1/0. The primary message is that mathematics applied as “approach” properly in the effort of explaining the Sunnatullah, and don’t make mathematics as a justification tool.

### 21 Responses

1. Subject: New comment item on http://rohedi.com
From: “Rohedi LAboratory”
Date: Sun, October 26, 2008 10:09 pm
To: rohedi@physics.its.ac.id
Priority: Normal
Options: View Full Header | View Printable Version | Download this as a file | View Message details | View as HTML

Hello rohedi,

A user has posted a new comment:

Author: vijay
Title: Bismillahirrahmanirrahim
Komentar: Sungguh sedikit sekali ilmu yang dimiliki oleh manusia, tidak akan pernah
mungkin layak untuk dibandingkan dengan ilmu Yang Maha Memiliki Ilmu.
Alhamdulillahi rabbil alamin,
sudah saatnya bagi umat Islam untuk berjihad dengan cara yang lebih cerdas dan islami.
Sesama manusia pun saya masih terlalu jauh untuk bisa berjihad seperti pak Ali Yunus
Rohedi, namun saya berterima kasih kepada Bapak, walau saya tidak begitu paham
melihat dan membaca artikel-artikel dari Bapak.
Allahu Akbar.

http://rohedi.com/content/view/33/1/

2. The truth of way

I am so interested with your letter, with mathematics we can explain about life, with mathematics we can learn how to manage we live. So, keep showing the truth of mathematics, to be a victor. God Bless You Mr.Rohedi.

3. I have written following two papers which may lead to the realisation for a higher theory of everything:

(i) Gravitation Force is the Ultimate Creator,
(1st Int. Conf. on Revival of Traditional Yoga, Lonavla Yoga Institute, Lonavla, January, 2006)
(ii) In Scientific Terminology, Source of Gravitational Wave is God
(2nd World Congress on Vedic Science, BHU, Varanasi, Feb 2007)
I have presented these two papers at the two different International Conferences. I am now submitting some views for being considered for Unified Field Theory

From Scriptures:
The Current which manifested in the beginning of the creation is the Current of Sabda (Sound) and of Chaitanya (Consciousness). From whom that Current issued forth is known as Soami (Supreme Being). This Current, by turning back can merge again in the Holy Feet of Supreme Being. The entire creation manifested from this current and is sustained with its energy and when the Current of the Holy Feet is withdrawn, the creation ceases to exist.This Current of the Holy Feet is the Reservoir of all energy, tastes and pleasures, knowledge, skill, shapes, forces and light etc. etc. and of the entire creation, is also the Creator of all of them.

From Science:
Gravitation Force is the cause of manifestation of the creation (birth of planets, stars), its sustenance and when it is withdrawn towards centre or source the entire creation ceases to exist. Photons have originated from gravitons. In black holes photons merge into gravitons. In Black Holes, Gravitational Force is so high that it does not allow even light to escape. What does it mean then? It simply means that the gravitational force at black-holes attracts light towards it with much greater velocity than the speed of light. In fact, all forces including electromagnetic force, material force (strong and weak nuclear force) all merge into gravitational force in black-holes and becomes one force there and when the creational process starts again from a Black-Hole all the forces appear (manifest) again and descends downwards to create billions of stars, planets, satellite, asteroids and various life forms.

Hence it can be assumed that the Current of Chaitanya (Consciousness) and Gravitational Wave are the two names of the same Supreme Essence (Seed) which has brought forth the entire creation.

Anirudh Kumar Satsangi,

All cosmological researches should be conducted keeping in view of the following philosophical facts:
It has been stated in Bible (John I-1) “In the beginning was the Word and the Word was with God, and the Word was God,”
The Radhasoami Religion also tells that, the ‘Word’ mentioned above is in fact Current of Sound or Current of Consciousness or Prime Current of Spirituality which was issued forth from its Source, or Creator or God. This Current has later on produced light and other forces. The scientists are discussing these days about dark energy which constitute about 96% of the entire universe which is not known to us. Only 4% part of the universe is known to us by all scientific means. In fact this 96% invisible portion of the universe is the vast expanse of spirituality which can be designated as field of gravitational waves in scientific terms. Visible portion of the universe (4%) consists of consciousness (gravitational force), mental force (electromagnetic waves) and material force (strong and weak nuclear force).
Body = Nuclear Force (weak as well as strong)
Mind = Electromagnetic Force.
Consciousness = Gravitation Force.
According to Radhasoami Religion the whole Universe can be sub-divided into three grand divisions viz.
1. Region of Pure Spirituality
2. Region of Subtle Maya
3. Region of Gross Maya
Nuclear forces dominate Region of Gross Maya (Gross Material Region), Electro-magnetic forces dominate Region of Subtle Maya (Subtle Material Region) and Gravitational Force dominates Pure Spiritual Region.
This is the only Truth which can be verified scientifically and can be termed as ‘higher theory for everything’. This also supports the statement of Sir Sahabji Maharaj the goal of science – Truth; the goal of philosophy – Ultimate Reality; and the goal of religion – God are the three names of same supreme essence.
1. Many things are common between Current of Consciousness and Gravitational Wave.
1. Current of consciousness can not be seen by any means and gravitational wave can also not be seen.
2. Current of consciousness is the weakest force on earth. Its strength goes on increasing on higher regions. Gravitational force is also very weak on earth and strong on Sun and even more stronger on black holes.
3 Tendency of both current of consciousness and gravitational waves are towards their source or centre.
4. Current of consciousness and gravitational force are both regarded as the creater of all the celestial and terrestrial bodies of the whole universe. They are also sustainer of these and when they turn back towards their source or centre the whole universe will collapse.
Hence it can be assumed that the source of current of consciousness and gravitational wave is the same i.e. God or ultimate creator.
This theory is based on scientific deduction. All other theories appear to be work of imaginative thinking and sometimes do not satisfy the criteria of scientific verification. In scientific terms it can be said that the ‘gravitons’ are the elementary
particle which was issued forth in the beginning of the creation accompanying with sound ‘Radha’
=====================================

Management of Obsessive Compulsive Disorder

Dear Editor

I read the above article by Dr Yatish Agarwal (October 2008). If we are able to understand the status of mind scientifically we will be able to cope all these problems more effectively. Mind and brain are two distinct things. Brain is anatomical entity whereas mind is functional entity. Mind can be defined as the function of autonomic nervous system (ANS). It is claimed that mind can be brought under conscious control through the practice of meditation. But how? ANS is largely under hypothalamic control which is situated very close to optic chiasma (sixth chakra or ajna chakra). Protracted practice of concentration to meditate at this region brings functions of ANS say mind under one’s conscious control.

ANS is further divided into parasympathetic nervous system (PSNS) and sympathetic nervous system (SNS). On the basis of these facts I have discovered a mathematical relationship for spiritual quotient (S.Q.). Spiritual Quotient can be expressed mathematically as the ratio of Parasympathetic dominance to Sympathetic dominance. PSNS dominates during meditative calm and SNS dominates during stress. In this formula we assign numerical values to the physiological parameters activated or suppressed during autonomic mobilization and put in the formula to describe the state of mind of an individual and also infer his/her level of consciousness.

Protracted practice of meditation under qualified guidance will help to manage all sort of psychological problems.

Emotional quotient can also be expressed mathematically as the product of Intelligence Quotient (I.Q.) and Wisdom Factor.

4. We can say that eq (4) and (5) are exactly the same since we can obtain (4) from (5) by simple substituion $t=2s$.

5. @watchmath

Of course I agree with you that the equality of the new tangent function in eq.(4) to the tangent function in eq.(5) can be verified as your recommended. I believe that eq.(5) only can be created geometrically (see Mathematics Handbook authorized by Stegun et.al). But look the equality of eq.(4) to the eq.(2) at t0=0 and y0=0, we will see that

sin(2t)/[1+cos(2t)] = sin(t)/cos(t) ,

and my GOD, substituting t=pi/2 into the above both sides, we as soon as say “Inna Lillahi” because mathematics ever inxactly as apprear from the result 0/0=1/0. Especially for this case, we must thank to Mr Hospital that have saved the mathematics via his L’Hospital theory. Apologize, I know this statement after visiting to this address:

http://masteranza.wordpress.com/2007/12/30/useful-tangent-triangle-identities/#comment-261

Wassalamu’alaikum.

Sincerely Yours

Rohedi/afasmt

6. “Al Islaamu ilmiyyun wa’amaliyyun” and “Al Islaamu ya’luu walaa yu’laa ‘alaihi”

So let we are thinking about universe, all knowledge, “Knowledge that was hidden” and the sign that was hidden.

Blackhole I think still mystery, we newer know the inside, coz we will trap on that. Event horizon is the beginner of the mystery … there is a “border” “barrier” “Hijab” as the obstacle between us and GOD, we need the “carrier” to GOD.

Where you gazed there at the face of the lord (Koran). I don’t mean that blackhole is GOD.

May GOD forgive me. wallahualam bi shawab.

7. @anirudh kumar satsangi

Congratulation you have develop the higher theory of everything more wonderful than which has been developed by Stephen Hawking. Hopefully your some views for being considered for Unified Field Theory are recognized by International Science Community, hence I soon read the fundamental aspect proposed by you.

Basically I agree with you and another that black holes has been central to our knowledge of the Universe. I remember Mr. Albert Einstein that after coming up with his general theory of relativity, the proof that black holes has been central to our knowledge of the Universe until now becomes the most of interest research. I also remember to
the team of scientists spent 16 years studying the existence of a super massive black hole thought to be at the centre of our galaxy, the Milky Way. While the black hole itself is invisible to the eye as described by brother Wahyu via leave comment previously. The team proved its existence by tracking the motions of 28 stars circling around it, that reveal information about forces at work at the galactic centre. Professor Reinhard Genzel the leader of the team said that “The stellar orbits in the galactic centre show that the central mass concentration of four million solar masses must be a black hole, beyond any reasonable doubt.” The astronomers were also able to measure with great accuracy how far the Earth is from the centre of the galaxy – a distance of 27,000 light years.

Of course the central region of the Milky Way is hard to see because the view from Earth is blocked by interstellar dust.
Recently, to overcome this problem, the astronomers, who published their findings in the Astrophysical Journal, focused on infrared light wavelengths that can penetrate the dust clouds. The team, who found that one particular star made a full orbit of the black hole in the 16 year study, now hope to use even more powerful telescopes to further test Einstein’s theories. A black hole is a theoretical region of space in which the gravitational field is so powerful that nothing, not even electromagnetic radiation (visible light), can escape its pull. They are believed to be the remnants of burnt out suns. And I think you need to joint them for justifying your Unified Field theory.

Once again congratulation and happy with Mr.Anirudh Kumar Satsangi.

8. o o o, thank’s.

9. @Anirudh Kumar Satsangi

There is similar view of me with you especially to your statement :

>In Black Holes, Gravitational Force is so high that it does >not allow even light to escape. What does it mean then? >It simply means that the gravitational force at black-holes >attracts light towards it with much greater velocity than >the speed of light. In fact, all forces including >electromagnetic force

You know that recently many researchers have been generating the wave which velocity greater than the speed of light. One of this can be seen at this address: quantumweird.wordpress.com/2007/07/23/thought-experiment-photons-at-radio-frequencies/

I believe that the effort can be succeeded if the Planck’s formula for black body radiation is considered in another form as I posted in this address:

http://eqworld.ipmnet.ru/forum/viewtopic.php?f=3&t=43&start=10

“The discussion about global warming has been commonly associated to the Planck’s Formula of Black Body Radiaton. We know that the Planck’s Formula for the internal energy of black body radiation is of form :

U(T) = ћω / [exp(ћω/(kT) – 1]

But when Einstein verified the phenomenon using harmonic oscillators, the above Planck’s Formula can only explain us that the energy difference between the sequence of two energy levels of harmonic oscillator is ћω. But if the internal energy is taken in the following form:

U(T) = 0.5ћω[ tanh{0.5ћω/(kT) – iП/2} – 1]

We will also verify that the minimum energy of the harmonic oscillator is 0.5ћω, and justifying that there are so many harmonic oscillators involved that known from П/2 as the phase differences representing between the two energy lavels. We know that the above of both U(T) is the internal energy of black body radiation in thermal equilibrum. Next question what ’s the form for non thermal equilibrum? Here, I give more information, that there is a possibility to include external perturbation to the differential equation representation of the above New Planck’s Formula.
Perhaps the New Planck’s Formula that can be useful to explain not only disclose confidential global warming but also in treating the experiment of regulated speed waves. If you and visitors here are interested to know the detail explanation about the alternative method of solving an ordinary differential equation, please visit to the above address :
%%%%%%%%%%

We know that theory of everything proposed by Stephen Hawking until now has not yet finished. Why? I believe he meets some difficulties especially in solving several mathematics model that required for finishing his unified field theory, once of this models is the general Klein Gordon . I have developed a new method of solving first order ODE so-called SMT (shortened from Sable Modulation Technique). The SMT succeeded in solving arctangent and Bernoulli differential equation or another first order ODE that can be transformed into both above DE’s. As explaining on the article “Fighting of the cause Allah by governing smart mathematics”, that the idea of developing this stable modulation technique based on the event of Isra’ and Mi’raj of prophet Muhammad. And apparently on my comment to another visitor, solving of dy/dt=1+y^2 by the SMT equal to the usual tangent function sin(2t)/[1+cos(2t)]=sin(t)/cos(t), but for t=pi/2 gives special feature that mathematics ever inexacly as shown in the equality of 0/0=1/0. Of course, now I am developing the SMT to solve not only for high order ODE’s, but also to Partial Differential Equation.

Mr. Anirudh Kumar Satsangi, at Indonesia there is also a similar effort of you in relating mathematical with spiritual quotient (S.Q), but in term of E.S.Q (Emmotional Spiritual Quotient) developed by Mr. Ary Ginanjar on ESQ Group.

Once again, I would like to thank for your appreciate by leaving a comment on my wordpress.

Sincerely,

Rohedi.

10. Dear All,
The following a small discussion me (Rohedi) with Jebavarde one of my colleague from Oxford University

From Oxford Math Overview 2009 :

Mansfield:

When f(x+y) = f(x)f(y), prove f(0) = 1 where f is a non-zero, real valued function.

rohedi – Friday 26th December, 2008 at 2:49 am :
Okay, now I will perform back substitution. The first function that satisfy the above equality is exponential function, thus we may write exp(x+y)=exp(x)exp(y). You are right because exp(0)=1. But can you show me another function?
%%%

jebavarde – Friday 26th December, 2008 at 4:53 pm
I’ve been thinking… to no avail. I’m thinking perhaps some function made of a combination of trigometric functions may exhibit this, since
cos(a+a) = 2cos(a)cos(a) – 1, and cos(0) = 1, which seems kind of close.
Considering the ‘opposite’ of this equality:
f(ab) = f(a) + f(b)
I have found two functions which satisfy this.
1. Obviously (it follows from your function) the logarithmic function: log(ab) = log(a) + log(b).
2. The arg function (argument of a complex number)
arg(zw) = arg(z) + arg(w)
I’ll think it over and try to find another function which satisfies the first.
%%%%

jebavarde – Friday 26th December, 2008 at 5:17 pm One function which does satisfy this, but is cheating somewhat, would be f(x) = 1
%%%

jebavarde – Friday 26th December, 2008 at 5:25 pm
Done some reading about, and apparently this is the ‘Cauchy Exponential Function’
%%%%

rohedi – Friday 26th December, 2008 at 10:04 pm
Really your statement not wrong, because you have introduced the word “when” in the front of f(x+y)=f(x)f(y). With the word “when” as the constrain, so your equality is always satisfied for x=0 and hence f(0)=1. Let we check for cosinus function,
cos(x+pi/2)=cos(x)cos(pi/2) , (1)
But we know from expand of the cosinus function that
cos(x+pi/2)=cos(x)cos(pi/2) – sin(x)sin(pi/2) , (2)
Thus, it is clearly that eq.(1) is obtained after cancel out the term of – sin(x)sin(pi/2) in eq.(2) because sin(0)=0. And somebody will agree with you that cos(0)=1 as the proof f(0)=1.
Okay, next we continue with expanding the left side of eq.(1)
cos(x+pi/2)=cos(x)cos(pi/2)
cos(x)cos(pi/2)-sin(x)sin(pi/2)=cos(x)cos(pi/2)
-sin(x)=cos(x)cos(pi/2)
finally,
-sin(x)=0,

We know that there so many values of x that satisfied the sin(x)=0, that are x=0, pi, 2pi, etc but only the even multiple of 2pi that satisfy cos(x)=1. Please take your conclusion to my explanation above.
Next, let consider the following example if the word “when” to be ignored from your statement
sin(x+pi/6)=sin(x)sin(pi/6)
%%%

rohedi – Friday 26th December, 2008 at 10:12 pm
Okay my special comment for this statement
%One function which does satisfy this, but is cheating % %somewhat, would be f(x) = 1

Let’s try this following function
f(x)=[V*sqrt(1-x)-arctan(sqrt(x/(1-x)))-arctan(sqrt((x+a)/(1-x)))]/pi

for any positive of a. You will never the value of x that satisfies f(x)=1 except for V>arctan(sqrt(a)).
Happy with you.
%%%%

rohedi – Saturday 27th December, 2008 at 7:54 am
Well, next I will explore more detail the following equality of

tan(x+pi/4)=[tan(x)+tan(pi/4)]/[1-tan(x)tan(pi/4)]
or
tan(x+pi/4)=[tan(x)+1]/[1-tan(x)], (1)

Let’s fill x=pi/4, then we have
tan(pi/2)=[tan(pi/4)+1]/[1-tan(pi/4)]
that gives :

1/0=2/0

Okay we agree to do not say that 1=2, isn’t it.
But let we change the tangent function for the left side with this

tan(t)=sin(2t)/[1+cos(2t)], (2)

hence we obtain the following equality 0/0=2/0, and what do you think withthis? I believe you will agree with me that without L’Hospital Theory, mathematics ever inexactly, isn’t it. Are you and all visitors here interested to learn more about how to create eq.(2) from arctangent differential equation dy/dt=1+y^2?
The new tangent function only can be create by using SMT (shortened from the stable modulation technique) that recently posted in this address :
http://eqworld.ipmnet.ru/forum/viewtopic.php?f=2&t=34&start=20
Please visit to the website maybe useful for you all.
%%%%

rohedi – Saturday 27th December, 2008 at 11:46 pm
My example of f(x) above is the equation of normalized dispersion relation of optical mode guided in a slab waveguide that has been commonly used in designing integrated optics for Photonics application. Please visit to the following address for detail explanation.

The simpliest method to obtain the x value of normalized optical mode propagation constant for every values of V and a that represent normalized thickness of the guide and the different ratio of refrative indices cover to the substrate of the guide respectively, is the secant method that needed two initial guesses x0 and x1. The following script of solving the dispersion relation for searching the value of x that I created using matlab. Maybe useful for you all here, let’s try the following scheme.

function x2=rohedi(func,a,V,x0,x1)
%script used in this routin called frohedi.m x2=x1-(x1-x0)feval(func,a,V,x1)/(feval(func,a,V,x1)-feval(func,a,V,x0));
while (abs(x2-x1)>=1e-16)
x0=x1;
x1=x2
x2=x1-(x1-x0)feval(func,a,V,x1)/(feval(func,a,V,x1)-feval(func,a,V,x0));
end
%%%%%
function y=frohedi(a,V,x) f=[V*sqrt(1-x)-atan(sqrt(x/(1-x)))-atan(sqrt((x+a)/(1-x)))]/pi;
y=f-1;
%%%%%

Important to be informed here that the value of x satisfied the dispersion relation : V*sqrt(1-x)=atan(sqrt(x/(1-x)))+atan(sqrt((x+a)/(1-x)))+pi;
is in the range of 0<x>a=1000;V0=atan(sqrt(a))+0.1; x0=0.9; x1=0.91;

If the searching value of x for every value of a is performed iteratively from V>atan(sqrt(a)), there are so many values of x that satisfy f(x)=1. This things to be proved by plotting the x-V curve.

V0=atan(sqrt(a))+0.1;Vf=16;step=0.1;
V=V0:step:Vf;
nV=length(V);
for k=1:nV
x(k)=rohedi(’frohedi’,a,V(k),x0,x1);
end
plot(V,x);

11. Mr.Rohedi, this is a recently news from TG Daily about New dark energy findings suggest Einstein’s theory is dead-on. Here I transtlate the resume into Indonesian Language

By Rick C. Hodgin
Tuesday, December 16, 2008 18:11

Washington(DC)-Hari ini NASA menggelar konferensi pers via telpon yang melaporkan temuan terbaru 3 ahli astrofisika tentang energi gelap. Mereka telah melihat secara jelas efek dari energi gelap itu pada benda yang paling massif di alam semesta ini. Bukti baru ini telah berpihak pada keyakinan para ilmuwan tentang 1)keberadaan energi gelap, 2) penjelasan mengapa alam semesta ini mengembang, dan 3) kebenaran teori relativitas umum Einstein selama memasukkan kontata kosmologi, padahal beliau pernah mengatakan telah melakukan apa yang disebutnya “kesalahan besar”.

Berita selengkapnya silahkan baca sendiri di
http://www.tgdaily.com/content/view/40607/113/.

12. I have a feeling that you think that equation $0/0=1/0$ that you obtain from your equation has a special meaning for you.
In fact the tan function is undefined at $t=\pi/2$. So both sides of the equation are undefined at $t=\pi/2$ and hence you can’t equate $0/0$ with $1/0$.

Regards,

13. @ wacthmath

He he he….are you seriously wants to discuss this topic in detail?

Okay, before discussing let’s you read the related references what you have. Of course including the references that explain the deference of NaN and not defined.

14. Here is from wikipedia:In computing, NaN, which stands for Not a Number, is a value or symbol that is usually produced as the result of an operation on invalid input operands, especially in floating-point calculations. For example, most floating-point units are unable to explicitly calculate the square root of negative numbers, and will instead indicate that the operation was invalid and return a NaN result.

So basically NaN is a symbol when a certain operation can’t be computed (my word). Mathematically $tan(\pi/2)$ is always undefined and so is $1/0$.

Again here some cases that can produce NaN according to wikipedia:
The following practices may cause NaNs:

* All mathematical operations with a NaN as at least one operand
* The divisions 0/0, ∞/∞, ∞/-∞, -∞/∞, and -∞/-∞
* The multiplications 0×∞ and 0×-∞
* The additions ∞ + (-∞), (-∞) + ∞ and equivalent subtractions.
* Applying a function to arguments outside its domain, including taking the square root of a negative number, taking the logarithm of a negative number, taking the tangent of an odd multiple of 90 degrees (or π/2 radians), or taking the inverse sine or cosine of a number which is less than -1 or greater than +1.

So in particular $0/0$ (the second case) and $pi/2$ (the last case) all produce NaN.

15. I meant $\tan \pi/2$ in my last post and not $\pi/2$.
You think that $tan(\pi/2)=\infty$ which is incorrect and I suspect that this misunderstand is rooted from the practice of highschool teacher teach this concept in Indonesia.
Let me stressed again $\tan(\pi/2)$ has no meaning, but we can talk about $\latex \lim_{x\to (\pi/2)^+}\tan x$ and $\lim_{x\to (\pi/2)} \tan x$

16. The last latex should read $\lim_{x\to (\pi/2)^+}\tan x$ and $\lim_{x\to (\pi/2)^-} \tan x$

17. @ watchmath

Oh suprise Sir,
So many thanks for your great efforts in searching the related references for our discussion here. I believe this will be useful not only for me, but also for my visitors.

But, before we continue this continue, I need your help again to search the book references and/or journals that presented the formula of tangent function

tan(t)=sin(2t)/[1+cos(2t)],

but sorry not in the form

tan(t/2)=sin(t)/[1+cos(t)]

as appear at your last post.

This is very important to prove whether my claim that tan(t)=sin(2t)/[1+cos(2t)] is the new formula for the tangent function that only can be created by using SMT.

Okay, I am still waiting you here. Thx.

18. @wacthmath

Sorry, I mean at the above phrase is the following sentence

But, before we continue this discussion…

19. What do you mean by created?
Your so called new formula for tangent as I said earlier is nothing but a simple substitution $t=2s$ from the second eq. So there is nothing special about your equation.
Or do you want something like this?
$\tan t=\sin t/\cos t=(2\sin t\cos t)/(2\cos^2 t)$
$=(2\sin t\cos t)/((\cos^2 t+\sin^2 t)+(\cos^2 t -\sin^2 t))=\sin(2t)/(1+\cos(2t) )$.

20. If you like tangent a lot, have you seen this in any textbook anywhere?
$\tan(t)=\frac{1-\cos(2t)}{\sin(2t)}$.
And of course this can’t be something new.
And surprise surprise if you plugin $\pi/2$ to the original eq. we get $1/0$ and if substitute to the latter we get $2/0$. So? Nothing important there, both of them are undefined and we can’t compare the two.

21. @watchmath

Apologise, I forgot to change Denaya Lesa’ address at leave comment before submitting the above reply comment. She is is my daughter. And we use the same computer for uploading comments.

Bye bye…
Afasmt/Rohedi