Question

Wnte the value of the expression $\tan \left(\frac{{\sin }^{-1}x+{\cos }^{-1}x}{2}\right),\mathrm{when}x=\frac{\sqrt{3}}{2}$

Answer 1

$$\begin{gathered} \tan \left(\frac{{\sin }^{-1}x+{\cos }^{-1}x}{2}\right)=\tan \left(\frac{\mathrm{\pi }}{4}\right)\left[\because {\sin }^{-1}x+{\cos }^{-1}x=\frac{\mathrm{\pi }}{2}\right] \\ =1 \end{gathered}$$