If $\tan^{-1}x + \tan^{-1}y + \tan^{-1}z = \pi$,then $x + y + z$ is equal to

If $\cot \frac{2x}{3} + \tan \frac{x}{3} = \csc \frac{kx}{3}$,then the value of $\tan^{-1}(\tan k)$ equals:

The value of $\cos \left(2 \cos ^{-1} x+\sin ^{-1} x\right)$ at $x=\frac{1}{5}$ is

$(\tan ^{-1} x)^2+(\cot ^{-1} x)^2=\frac{5 \pi^2}{8} \Rightarrow x=$

If $\frac{\sin ^{-1} x}{a}=\frac{\cos ^{-1} x}{b}=\frac{\tan ^{-1} y}{c}$ and $0 < x < 1,$ then the value of $\cos \left(\frac{\pi c}{a + b}\right)$ is

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