JEE MAIN - Mathematics (2024 - 9th April Evening Shift - No. 29)
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 __________.
Answer
0
Explanation
$$\begin{aligned} & 2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5} \\ & \frac{\pi}{2}+\cos ^{-1} x=\frac{2 \pi}{5} \\ & \cos ^{-1} x=\frac{2 \pi}{5}-\frac{\pi}{2} \\ & \cos ^{-1} x=\frac{-\pi}{10} \end{aligned}$$
Which is not possible as $$\cos ^{-1} x \in[0, \pi]$$
$$\therefore \quad$$ No solution
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