$$cos$$−$$1a$$−xa−$$b=$$$$sin$$−$$1x$$−ba−$$b(a$$≠$$b)is$$ possible if

Correct option is 1a≥x≥bora≤x≤b

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$\cos^{- 1} \sqrt{\frac{a - x}{a - b}} = \sin^{- 1} \sqrt{\frac{x - b}{a - b}} (a \neq b)$ is possible if

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a≥x≥bora≤x≤b

a=x=b

a>bAnd x takes any value

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detailed solution

Correct option is A

Take a−xa−b=x−ba−b=12Then a-xa-b=12 ⇒2a-2x=a-b ⇒x=a+b2 ⇒a≤x⩽b or a≥x≥b

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cos−1a−xa−b=sin−1x−ba−b(a≠b)is possible if

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$\cos^{- 1} \sqrt{\frac{a - x}{a - b}} = \sin^{- 1} \sqrt{\frac{x - b}{a - b}} (a \neq b)$ is possible if