Advertisements
Advertisements
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`
shaalaa.com
Is there an error in this question or solution?