Question:medium

The value of \( x \) which satisfies the equation \( \sin^{-1}\left(\frac{2}{3}\sqrt{1 - x^2}\right) = \cot^{-1}\left(2\sqrt{x}\right) \), is

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When an equation looks algebraically heavy, plug in the options. Since \(x\) is under a square root (\(2\sqrt{x}\)), \(x\) must be a perfect square, which immediately narrows your choices to \(1/4\) and \(1/9\).

Updated On: Apr 8, 2026

\(\frac{1}{2}\)
\(\frac{1}{4}\)
\(\frac{1}{8}\)
\(\frac{1}{9}\)

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The Correct Option is D

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The value of \( x \) which satisfies the equation \( \sin^{-1}\left(\frac{2}{3}\sqrt{1 - x^2}\right) = \cot^{-1}\left(2\sqrt{x}\right) \), is

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The Correct Option is D

Solution and Explanation

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