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Solution of the equation $\tan (\cos^{- 1} x) = \sin (\cot^{- 1} \frac{1}{2})$ is

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x=±73

x=±53

x=±352

none of these

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Correct option is B

We have, tan⁡cos−1⁡x=sin⁡cot−1⁡12⇒tan⁡tan−1⁡1−x2x=sin⁡tan−1⁡2⇒tan⁡tan−1⁡1−x2x=sin⁡sin−1⁡21+4⇒tan⁡tan−1⁡1−x2x=sin⁡sin−1⁡25⇒1−x2x=25⇒51−x2=4x2⇒9x2=5,∴x=±53.

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Solution of the equation tan⁡cos−1⁡x=sin⁡cot−1⁡12 is

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Solution of the equation $\tan (\cos^{- 1} x) = \sin (\cot^{- 1} \frac{1}{2})$ is