Question

find x if sec^-1(√2)+cosec^-1x=π/2​

Answer 1

$clearely \\ { \sec( \sqrt{2} ) }^{ - 1} + { \cosec(x) }^{ - 1} = \frac{\pi}{2} \\ { \cosec(x) }^{ - 1} = \frac{\pi}{2} - { \sec( \sqrt{2} ) }^{ - 1} \\ = \frac{\pi}{2} - \frac{\pi}{4} \\ = \frac{\pi}{4} \\ { \cosec(x) }^{ - 1} = \frac{\pi}{4} \\ x = { \cosec( \frac{\pi}{4} ) }^{ - 1} \\ x = \frac{\pi}{4}$