If $\cos ^{-1} x=\tan ^{-1} x$, then $\sin \left(\cos ^{-1} x\right)=$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

\cos ^{-1} x=\tan ^{-1} x

, then

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

View answer and explanation

Correct option: B

x^2

Option B (

x^2

) is correct because, by setting

\cos^{-1}x = \tan^{-1}x = \theta

, we derive the relationship

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

through trigonometric identities.

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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},

{\tan ^{ - 1}}\left( {\frac{{xy}}{{zr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{yz}}{{xr}}} \right) + {\tan ^{ - 1}}\left( {\frac{{xz}}{{yr}}} \right)\;

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