$\cos \left( \sin^{-1} \frac{5}{13} \right) = $

$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

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

If $\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$,then $\cos^{-1}(\sin \theta)$ is equal to

If ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$,then $x =$

If the area of the region bounded by the parabola $y^2 = 4kx$ and the line $x = k$, (where $k > 0$) is $\frac{128}{3}$ sq. units, then the value of $\sin^{-1} \left( \frac{2}{k} \right)$ is equal to...