If $3 \tan ^{-1} \frac{1}{2+\sqrt{3}}-\tan ^{-1} \frac{1}{x}=\tan ^{-1} \frac{1}{3}$ then $x=$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

1 of 1

Application +4 | -1

3 \tan ^{-1} \frac{1}{2+\sqrt{3}}-\tan ^{-1} \frac{1}{x}=\tan ^{-1} \frac{1}{3}

then

x=

View answer and explanation

Correct option: A

Option A (2) is correct because by simplifying the inverse trigonometric equation using

\tan 15^{\circ}=2-\sqrt{3}

and the formula for

\tan^{-1}x - \tan^{-1}y

, we find that

x=2

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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)