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The value of sin^(-1)[xsqrt(1-x)-sqrt(x)...

The value of `sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)]` is equal to

A

`sin^(-1) x + sin^(-1) sqrtx`

B

`sin^(-1) x - sin^(-1) sqrtx`

C

`sin^(-1) sqrtx - sin^(-1) x`

D

none of these

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( \sin^{-1}[x\sqrt{1-x} - \sqrt{x}\sqrt{1-x^2}] \). ### Step-by-Step Solution: 1. **Identify the Expression**: We start with the expression: \[ \sin^{-1}[x\sqrt{1-x} - \sqrt{x}\sqrt{1-x^2}] ...
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