sin - 1 ( x 1 - x - x 1 - x 2 ) =

Question

$\sin^{- 1} (x \sqrt{1 - x} - \sqrt{x} \sqrt{1 - x^{2}}) = \dots \dots \dots \dots$

Smart Achievers · Accepted Answer

(2)

Ans. $s i n^{- 1} x - s i n^{- 1} \sqrt{x}$

Explanation:

We know that

$\sin^{- 1} (x \sqrt{1 - x} - \sqrt{x} \sqrt{1 - x^{2}})$

$= \sin^{- 1} (x \sqrt{1 - {(\sqrt{x})}^{2}} - \sqrt{x} \sqrt{1 - x^{2}})$

$= \sin^{- 1} x - \sin^{- 1} \sqrt{x}$

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