Question

Find the principal value of ${\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$.

Answer 1

Let, $x=si{n}^{-1}\frac{1}{\sqrt{2}}$

the principal value of $si{n}^{-1}x$ lies in [ $-\frac{\pi }{2},\frac{\pi }{2}$]

=> $sinx=\frac{1}{\sqrt{2}}$

=> Therefore, $x=\frac{\pi }{4}$