JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Hard

1 of 1

Application +4 | -1

\tan \left[\frac{1}{2} \cos ^{-1}\left(\frac{\sqrt{5}}{3}\right)\right]

is equal to

View answer and explanation

Correct option: A

\frac{3-\sqrt{5}}{2}

Option A (

\frac{3-\sqrt{5}}{2}

) is correct because using the half-angle formula for tangent and simplifying the expression leads to the correct answer.

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\sin \left(2 \tan ^{-1}(1 / 3)\right)+

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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)