`sin^(-1)""(sin""(3pi)/(5))` का मान ज्ञात कीजिए ।

Explanation

Let `sin^(-1)(sin.(3pi)/(5))=y`.
`therefore sin y = sin. (3pi)/(5)`, where `-(pi)/(2) le y le (pi)/(2)`.
But `y=(3pi)/(5)` does not satisfy `-(pi)/(2) le y le (pi)/(2)`.
Hence , we have to find the value of y which satisfies `- (pi)/(2) le y le (pi)/(2)`.
`because (3pi)/(5)= pi -(2pi)/(5)`,where `(2pi)/(5) in [(-pi)/(2),(pi)/(2)]`
`therefore sin y = sin (pi-(2pi)/(5))= sin.(2pi)/(5)`
`therefore y=(2pi)/(5)" " therefore sin^(-1)(sin.(3pi)/(5))=(2pi)/(5)`.