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If $a \sin^{- 1} x - b \cos^{- 1} x = c$ then the value of $a \sin^{- 1} x + b \cos^{- 1} x =$

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π2

π ab+cb−aa+b

π ab+ca−ba+b

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detailed solution

Correct option is D

Given asin−1x−bcos−1x=c →1We know that asin−1x+acos−1x=aπ2 →2Also bsin-1x+bcos-1x=bπ2 →3Now equatioins 2-1⇒ Cos−1x=aπ2−ca+band equations 3+1⇒sin-1x=bπ2+ca+b∴ asin−1x+b cos−1x=πab+ca−ba+b

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Ifasin−1x−b cos−1x=c then the value of asin−1x+bcos−1x=

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Ready to Test Your Skills?

free study material

If $a \sin^{- 1} x - b \cos^{- 1} x = c$ then the value of $a \sin^{- 1} x + b \cos^{- 1} x =$