If sin^-1 x - cos^-1 x = π/6, then x = A. 1/2 B. √3/2 C. -1/2 D. none of these

Question

If sin^-1 x - cos^-1 x = \(\frac{\pi}6\), then x =

A. \(\frac 12\)

B. \(\frac{\sqrt3}2\)

C. -\(\frac 12\)

D. none of these

Answer 1

Correct option is B.\(\frac{\sqrt3}2\)

We are given that,

sin^-1x - cos^-1x = \(\frac{\pi}6\).....(i)

We need to find the value of x.

By using the property of inverse trigonometry,

sin^-1x + cos^-1x = \(\frac{\pi}2\)

We can find the value of sin^-1x in the terms of cos^-1x.

⇒ sin^-1x = \(\frac{\pi}2\) - cos^-1x

Substituting the value of sin^-1x in equation (i),