If $\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}$, then $x$ is equal to

Neither $\frac{2}{3}$ nor $-\frac{2}{3}$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}

, then

x

is equal to

View answer and explanation

Correct option: C

\frac{2}{3},-\frac{2}{3}

Option C (

\frac{2}{3}, -\frac{2}{3}

) is correct because solving the trigonometric equation

\cos(2\sin^{-1}x) = \frac{1}{9}

yields both positive and negative solutions for x.

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