@MartinSleziak I am a bit surprised to see the post about Mathematica in the close votes review queue.

In this solution: topperlearning.com/doubts-solutions/…

If you put the value of x that we obtain in the LHS and RHS, you don't get the same value

What's going on here?

See wolframalpha.com/input/?i=sin(cot%5E-1(-1%2F2)) and wolframalpha.com/input/?i=cos(tan%5E-1(-1%2F2))

@rahuldottech When I try your link, I get "access denied".

You don't have permission to access "http://www.topperlearning.com/doubts-solutions/solve-for-x-sin-cot-1-x-1-cos-ta‌​n-1x-4ntoqsll" on this server

What is actually the question?

Here is Google Cache: webcache.googleusercontent.com/search?q=cache:https://…

So the problem seems to be $\sin[\cot^{-1}(x+1)]=\cos(\tan^{-1}x)$

@MartinSleziak appears to be georestricted. One sec

@MartinSleziak yep

They use $\tan^{-1}A=\cos^{-1}\frac1{\sqrt{1+A^2}}$. Which is derived from $\cos x=\frac1{\sqrt{1+\tan^2x}}$.

It is true that $|\cos x|=\left|\frac1{\sqrt{1+\tan^2x}}\right|$. But without absolute value this is not true for each $x$.

wolframalpha.com/input/?i=cos(x),+1%2Fsqrt(1%2Btan%5E2(x))

wolframalpha.com/input/…

Possibly you might decide noty to worry about the signs and solve this with absolute values. And then throw away the solutions where the signs are opposite.

BTW this would be more suitable fro Mathematics - either the main chatroom or some of the other rooms. (Possibly Basic Mathematics.‌​)

Meta: Differences between mathoverflow and math.stackexchange.

@MartinSleziak whoa so I'm unfamiliar with that syntax, and I'm not sure what to make of those Wolfram inputs (they appear to be beyond what I've been taught), but I think I understand what you're saying

Some related question on Mathematics: Simplifying a trigonometric expression: $\cos(\tan^{-1}x)$ and Simplify $\sin^3{\left(\cot^{-1}{\left(x\right)}\right)}$

@MartinSleziak ah, my bad. Thanks. I'll ask there.

Thanks for all the help

The WolframAlpha links are simply to show that the functions we are talking about have different graphs. (They are equal only for some inputs.)

The syntax such as \frac1{\sqrt{1+\sin^2x} and similar is MathJax/LaTeX. If you plan to use Mathematics site, you'll need it.

It is not rendered by default in chat, but you can get it rendered if needed.

I'll copy-paste the instructions from elsewhere:

ust a reminder - to read MathJax/LaTeX in chat you can use the bookmarklet mentioned in this post on meta or go directly to robjohn's website: math.ucla.edu/~robjohn/math/mathjax.html

In any case, if this is your only chat about mathematics, you probably won't be needing that.

Sorry for using MathJax without asking first whether you can read it. People who discuss mathematics in chat typically use some kind of bookmarklet to get it rendered similarly as in posts.

@MartinSleziak I figured that it's a variation of LaTeX, I just don't know it

@MartinSleziak okok thanks

That was a post from the first day of this room. (Before my time here.)

BTW MO reached 50000 question in May 2014: chat.stackexchange.com/transcript/9369/2014/5/4 Now it is over 100k.