The value of $\cos (2{\cos ^{ - 1}}x + {\sin ^{ - 1}}x)\;{\rm{at}}\;x = \frac{1}{5}\;$ is

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

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Application +4 | -1

The value of

\cos (2{\cos ^{ - 1}}x + {\sin ^{ - 1}}x)\;\mathrm{at}\;x = \frac{1}{5}\;

View answer and explanation

Correct option: D

- \frac{{2\sqrt 6 }}{5}

Option D (

- \frac{{2\sqrt 6 }}{5}

) is correct because it involves simplifying the expression using trigonometric identities and substituting the given value of x.

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\cos ^{-1}(\cos 12)-\sin ^{-1}(\sin 12)

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\cos ^ {-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9 \pi}{10}-\sin \frac{9 \pi}{10}\right)\right\}=

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

x

{x^2} + {y^2} + {z^2} = {r^2},

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