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If -12≤x≤12 then sin-1(2x1-x2) is equal to -

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Question

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

Options

  • `2sin^-1x`

  • `sin^-1x`

  • `sqrt(sin^-1x)`

  • none of these

MCQ

Solution

`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`

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