If $\sin^{-1} x + \sin^{-1} y = \pi/2$, then $x^2$ is equal to

Evaluate: $\cos^{-1}(\cos \frac{4\pi}{3}) + \sin^{-1}(\sin \frac{4\pi}{3}) = \dots$

$\cot ^{-1}\left(\frac{1}{\sqrt{x^2-1}}\right)=$ . . . . . . where,$x>1$.

If $\cos^{-1} x - \cos^{-1} \frac{y}{2} = \alpha$,then $4x^2 - 4xy \cos \alpha + y^2$ is equal to

If $2 \sin ^{-1} x-3 \cos ^{-1} x=4, x \in[-1,1]$,then $2 \sin ^{-1} x+3 \cos ^{-1} x$ is equal to

If $x_1, x_2, x_3$ are the real roots of the equation $x^3-x^2 \tan \theta+x \tan ^2 \theta+\tan \theta=0$ and $0 < \theta < \frac{\pi}{4}$,then the value of $\tan ^{-1} x_1+\tan ^{-1} x_2+\tan ^{-1} x_3$ at $\theta=\frac{\pi}{12}$ is