If $\tan ^{-1} x + \tan ^{-1} y + \tan ^{-1} z = \frac{\pi}{2}$,where $x, y, z > 0$ and $xy < 1$,then the value of $xy + yz + zx$ is:

The value of $\tan \left[2 \tan ^{-1} \frac{1}{5}-\frac{\pi}{4}\right]$ is

Find $\frac{dy}{dx}$ for $y = \cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)$,where $0 < x < 1$.

$\sin^{-1} \sqrt{\frac{x}{x+a}}$ is equal to

The sum to infinite terms of the series $\tan^{-1}\left(\frac{1}{3}\right) + \tan^{-1}\left(\frac{2}{9}\right) + \dots + \tan^{-1}\left(\frac{2^{n-1}}{1+2^{2n-1}}\right) + \dots$ is

$\cos \left[ 2\cos^{-1}\frac{1}{5} + \sin^{-1}\frac{1}{5} \right] = $