The value of ${\tan ^{ - 1}}\frac{1}{2} + {\tan ^{ - 1}}\frac{1}{3} + {\tan ^{ - 1}}\frac{7}{8}$ is

${\tan ^{ - 1}}\frac{{25}}{{24}}$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

1 Easy

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Application +4 | -1

The value of

{\tan ^{ - 1}}\frac{1}{2} + {\tan ^{ - 1}}\frac{1}{3} + {\tan ^{ - 1}}\frac{7}{8}

View answer and explanation

Correct option: C

{\tan ^{ - 1}}15

The correct answer is C (

{\tan ^{ - 1}}15

) because it results from applying the arctangent addition formula twice to simplify the expression.

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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)