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Inverse Trigonometric Functions question

2023 · Shift 2 · Q20

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PYQ Library
JEE Advanced
Mathematics
Inverse Trigonometric Functions
2023 · Shift 2 · Q20

Inverse Trigonometric Functions question

2023 · Shift 2 · Q20

JEE AdvancedMathematicsInverse Trigonometric FunctionsMCQ+3 / −1

For any

y \in \mathbb{R}

, let

\cot ^{-1}(y) \in(0, \pi)

and

\tan ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)

. Then the sum of all the solutions of the equation

\tan ^{-1}\left(\frac{6 y}{9-y^2}\right)+\cot ^{-1}\left(\frac{9-y^2}{6 y}\right)=\frac{2 \pi}{3}

for

0\lt |y|\lt 3

, is equal to :

A
$2 \sqrt{3}-3$
B
$3-2 \sqrt{3}$
C
$4 \sqrt{3}-6$
D
$6-4 \sqrt{3}$

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