Inverse Trigonometric Functions

The principal value of $\tan\,^{-1}\left(cot\frac{43\pi\,}{4}\right)$ is

A value of $x$ satisfying the equation $\sin\,\left[\cot\,^{-1}\left(1+x\right)\right]=\cos\,\left[\tan\,^{-1}x\right],$ is:

If the sum of all the solutions of $\tan\,^{-1}\left(\frac{2x}{1-x^{2}}\right)+\cot\,^{-1}\left(\frac{1-x^{2}}{2x}\right)=\frac{\pi\,}{3}$,$-1<x<1,x\neq\,0$, is $\alpha\,-\frac{4}{\sqrt{3}}$, then $\alpha\,$ is equal to…

For $x\in\,(-1,1]$, the number of solutions of the equation $\sin\,^{-1}x=2\tan\,^{-1}x$ is equal to

The value of $\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{1}{7}\right)$ is equal to

If $k$ is a root of $x^2 - 4x + 1 = 0$, then what is $\tan^{-1}k + \tan^{-1}\dfrac{1}{k}$ equal to?

What is the slope of the tangent of $y=\cos ^{-1}(\cos x)$ at $x=-\frac{\pi}{4} ?$

If $4 \sin ^{-1} x+\cos ^{-1} x=\pi$, then what is $\sin ^{-1} x+4 \cos ^{-1} x$ equal to?

Let $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$ for $0 \leq x, y, z \leq 1$. What is the value of $x^{1000}+y^{1001}+z^{1002}$ ?

The equation $\sin ^{-1} x-\cos ^{-1} x=\frac{\pi}{6}$ has

If $\sin ^{-1} \frac{2 p}{1+p^2}-\cos ^{-1} \frac{1-q^2}{1+q^2}=\tan ^{-1} \frac{2 x}{1-x^2}$, then what is $x$ equal to ?

If $3 \sin ^{-1} x+\cos ^{-1} x=\pi$, then what is $x$ equal to?