If `sin^(-1)x - cos^(-1) x = (pi)/(6)`, then what is the value of x ?

Options

A. `x = -(1)/(2)`
B. x = 1
C. `x = (1)/(2)`
D. `x = (sqrt(3))/(2)`

Answer

D

Explanation

As given :
`sin^(-1)x - cos^(-1)x=(pi)/(6)" "...(1)`
and we know that `sin^(-1)x + cos^(-1)x = (pi)/(2)" ...(2)`
On adding Eqs. (1) and (2) we get
`2 sin^(-1)x=(pi)/(6)+(pi)/(2)=(2pi)/(3)`
`rArr sin^(-1)x=(pi)/(3)rArr x="sin"(pi)/(3)=(sqrt(3))/(2)`