Find the principal value of each of the following: (i)`sin^(-1)1/2-2sin^(-1)1/(sqrt(2))` `"""""`(ii) `sin^(-1){cos(sin^(-1)(sqrt(3/2))}`

Explanation

(i) `sin^-1 (1/2) - 2sin(1/sqrt2) = pi/6 - 2(pi/4) `

`=> pi/6 - pi/2 = -pi/3`

(ii) `sin^-1 {cos (sin^-1 (sqrt3/2))} = sin^-1 (cos (pi/3)) `

`= sin^-1 (1/2) = pi/6`

Answer