$$ \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)= $$

$2 \cos ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ is valid for all values of ' $x$ ' satisfying

Let $f: R \rightarrow R$ be given $f(x)=\tan x$. Then, $f^{-1}(1)$ is

If $\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$, then $x(y+z)+y(z+x)+z(x+y)$ equals to