Q51 / 90 · JEE Main 2024 (09 Apr Shift 2) · Mathematics

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5}$, is _______

Correct answer: 0

Solution

$\begin{aligned} & 2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5} \\ & \Rightarrow \quad \pi+\cos ^{-1} x=\frac{2 \pi}{5} \\ & \Rightarrow \quad \cos ^{-1} x=\frac{-3 \pi}{5} \end{aligned}$
Not possible Ans. 0

Hence, the correct answer is 0.

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