List of top Mathematics Questions on Properties of Inverse Trigonometric Functions asked in BITSAT

The value of $\cos \left[ \frac{1}{2} \cos^{-1}\left(\cos\left(\sin^{-1} \frac{\sqrt{63}}{8}\right)\right)\right] $ is -

The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is