$\sin \left[3 \sin ^{-1}(0.4)\right] = \ldots$

The number of solutions of $\tan^{-1}4x + \tan^{-1}6x = \frac{\pi}{6}$ where $-\frac{1}{2\sqrt{6}} < x < \frac{1}{2\sqrt{6}}$ 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:

The value of $\tan \left\{\frac{1}{2} \cos ^{-1} \frac{\sqrt{5}}{3}\right\}$ is

If $y = \tan^{-1} \sqrt{\frac{1 + \cos x}{1 - \cos x}}$,then $\frac{dy}{dx}$ is

If $\tan^{-1} \frac{a+x}{a} + \tan^{-1} \frac{a-x}{a} = \frac{\pi}{6}$,then $x^2 =$