For any y ∈ , let cot –1 ( y ) ∈ (0, π) and an ^ -1 (y) (- 2 , 2 ) . Then the sum of all…
Mathematics · JEE Advanced · NTA Exams — Trigonometry
For any y ∈ 
, let cot–1 (y) ∈ (0, π) and
\(\ an ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) .\)
Then the sum of all the solutions of the equation
\(\ an ^{-1}\left(\frac{6 y}{9-y^{2}}\right)+\cot ^{-1}\left(\frac{9-y^{2}}{6 y}\right)=\frac{2 \pi}{3}\)for 0 < |y| < 3, is equal to
, let cot–1 (y) ∈ (0, π) and \(\ an ^{-1}(y) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) .\)
Then the sum of all the solutions of the equation
\(\ an ^{-1}\left(\frac{6 y}{9-y^{2}}\right)+\cot ^{-1}\left(\frac{9-y^{2}}{6 y}\right)=\frac{2 \pi}{3}\)for 0 < |y| < 3, is equal to
Answer
(A)
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