Question

find the principal value of
${ \sin( \frac{1}{ \sqrt{2} } ) }^{ - 1}$
​

Answer 1

$\huge\underline\bold\red{★Answer★}$

$let \: \: \: y = {sin}^{ - 1} ( \frac{1}{ \sqrt{2} } ) \\ siny = \frac{1}{ \sqrt{2} } \\ y = \frac{\pi}{4} \\ since \: \: range \: \: of \: \: {sin}^{ - 1} \: is \: - \frac{\pi}{2} \leqslant x \leqslant \frac{\pi}{2} \\ \therefore \: \: principal \: \: value \: \: of \: \: {sin}^{ - 1} ( \frac{1}{ \sqrt{2} } ) \: \: is \: \: \frac{\pi}{4}$