JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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Application +4 | -1

Value of

\sin ^{-1}\left\{\sin \left[\cos ^{-1}\left(\cos \left\{\sin ^{-1}\left[\sin \left(\frac{3 \pi}{4}\right)\right]\right\}\right)\right]\right\}

equals

View answer and explanation

Correct option: C

\frac{\pi}{4}

Option C (

\frac{\pi}{4}

) is correct because simplifying the nested trigonometric and inverse trigonometric functions leads to the final value of

\frac{\pi}{4}

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\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1

x

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2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right)