Question:
Wnte the value of the expression $\tan \left(\frac{\sin ^{-1} x+\cos ^{-1} x}{2}\right)$, when $x=\frac{\sqrt{3}}{2}$
Solution:
$\tan \left(\frac{\sin ^{-1} x+\cos ^{-1} x}{2}\right)=\tan \left(\frac{\pi}{4}\right)$ $\left[\because \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}\right]$
$=1$