Wnte the value of the expression

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:

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

$=1$

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