The value of ${\cot ^{ - 1}}\frac{3}{4} + {\sin ^{ - 1}}\frac{5}{{13}}$ is

${\sin ^{ - 1}}\frac{{12}}{{13}}$

${\sin ^{ - 1}}\frac{{65}}{{68}}$

JEE MATHEMATICS MCQ: INVERSE TRIGONOMETRY

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The value of

{\cot ^{ - 1}}\frac{3}{4} + {\sin ^{ - 1}}\frac{5}{{13}}

View answer and explanation

Correct option: A

{\sin ^{ - 1}}\frac{{63}}{{65}}

Option A is correct because by converting both terms to arcsin and using the arcsin addition formula, the expression simplifies to

{\sin ^{ - 1}}\frac{{63}}{{65}}

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