If S is the sum of the first 10 terms of the series
$\tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{7}\right)+\tan ^{-1}\left(\frac{1}{13}\right)+\tan ^{-1}\left(\frac{1}{21}\right)+\ldots \ldots$
then tan(S) is equal to :

If $\cos ^{-1} x-\cos ^{-1} \frac{y}{2}=\alpha$, where $1 \leq x \leq 1,-2 \leq y \leq 2$, $x \leq \frac{y}{2}$, then for all $...

All $x$ satisfying the inequality $\left(\cot ^{-1} x\right)^2-7\left(\cot ^{-1} x\right)+10>0$, lie in the interval

The value of $\cot \left(\sum_{n=1}^{19} \cot ^{-1}\left(1+\sum_{p=1}^n 2 p\right)\right)$ is

The domain of the function $f(x)=\sin ^{-1}\left(\frac{3 x^2+x-1}{(x-1)^2}\right)+\cos ^{-1}\left(\frac{x-1}{x+1}\right)$ is :

If $\cos ^{-1}\left(\frac{2}{3 x}\right)+\cos ^{-1}\left(\frac{3}{4 x}\right)=\frac{\pi}{2}\left(x>\frac{3}{4}\right)$, then $x$ is equal to :

If $\sum_{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=P$, then the value of $\tan p$ is :

If $2 y=\left(\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right)^2, x \in\left(0, \frac{\pi}{2}\right)$ then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to:

$\cos ^{-1}(\cos (-5))+\sin ^{-1}(\sin (6))-\tan ^{-1}(\tan (12))$ is equal to :