Question

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

Answer 1

$\mathrm{We}\mathrm{know}\mathrm{that}{\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2},\mathrm{for}\mathrm{all}x\in \left(-1,1\right]\mathrm{Therefore},\tan \left(\frac{{\sin }^{-1}x+{\cos }^{-1}x}{2}\right)=\tan \left(\frac{\left(}{\frac{\pi }{2}}\right)=\tan \left(\frac{\pi }{4}\right)=1.$