The equation `sin^(-1)(3x - 4x^(3)) = 3 sin^(-1) (x)` is true for all value of x lying in which one of the following intervals ?

Options

A. `[-(1)/(2), (1)/(2)]`
B. `[(1)/(2),1]`
C. `[-1, -(1)/(2)]`
D. `[-1, 1]`

Answer

D

Explanation

Let `sin^(-1) x = theta rArr x = sin theta`
`sin^(-1)(3 sin theta - 4 sin^(3) theta)=sin^(-1) sin 3 theta = 3 theta = 3 sin^(-1)x` Equation `sin^(-1)(3x - 4x^(3))=3 sin^(-1)x` is true for all values of x lying in the interval [-1, 1].