Question

If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to

पर्याय

• `2sin^-1x`

• `sin^-1x`

• `sqrt(sin^-1x)`

• none of these

Answer 1

`2sin^-1x`

Explanation:

Let x = sin θ

Then `sin^-1` x = θ

We have `(2xsqrt(1 - x^2)) = sin^-1 (2 sin theta sqrt(1 - sin^2 theta))`

= `sin^-1 (2sintheta costheta)`

= `sin^-1 (sin 2theta)`

= `2theta`

= `2sin^-1x`