Question

The value of `sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))),` where `x in (pi/2,pi)` , is equal to `pi/2` (b) `-pi` (c) `pi` (d) `-pi/2`
A. `(pi)/(2)`
B. `-pi`
C. `pi`
D. `-(pi)/(2)`

Answer 1

Correct Answer - D
`sin^(-1) (cos (cos^(-1) (cos x) + sin^(-1) (sin x)))`
`= sin^(-1) (cos (x + pi - x)) " " ["as " x in (pi//2)]`
`= sin^(-1) (cos pi) = sin^(-1) (-1) = -(pi)/(2)`