The value of $\sin ^{-1}\left[\cos \left(\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right)\right]$ is $\pi / k$; then find the value of $k$.

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

The value of

\sin ^{-1}\left[\cos \left(\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right)\right]

\pi / k

; then find the value of

k

View answer and explanation

Correct option: A

Option A (4) is correct because the expression simplifies to

\sin^{-1}(\cos(\frac{\pi}{4})) = \sin^{-1}(\frac{\sqrt{2}}{2}) = \frac{\pi}{4}

, thus k=4.

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