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