If $\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$,where $-1 \leq x \leq 1$,$-3 \leq y \leq 3$,and $x \leq \frac{y}{3}$,then for all $x, y$,$9 x^2-6 x y \cos \alpha+y^2$ is equal to

$\tan ^{-1} 2 + \tan ^{-1} 3 = $

If $(\sin ^{-1} x)^{2}-(\cos ^{-1} x)^{2}=a ; 0 < x < 1, a \neq 0$,then the value of $2 x^{2}-1$ is :

$\sec(\text{cosec}^{-1}x)$ is equal to

The value of $\sin ^{-1}\left(-\frac{1}{\sqrt{2}}\right)+\cos ^{-1}\left(-\frac{1}{2}\right)-\cot ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\tan ^{-1}(\sqrt{3})$ is:

If $\alpha > \beta > \gamma > 0$,then the expression $\cot ^{-1}\left\{\beta+\frac{(1+\beta^2)}{(\alpha-\beta)}\right\}+\cot ^{-1}\left\{\gamma+\frac{(1+\gamma^2)}{(\beta-\gamma)}\right\}+\cot ^{-1}\left\{\alpha+\frac{(1+\alpha^2)}{(\gamma-\alpha)}\right\}$ is equal to: