Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin^-1x+3cos^-1x=2π/5

Question

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 1

Correct answer is : 0 

\(2 \sin ^{-1} x+3 \cos ^{-1} x=\frac{2 \pi}{5}\)

\(\Rightarrow \quad \pi+\cos ^{-1} x=\frac{2 \pi}{5}\)

\(\Rightarrow \quad \cos ^{-1} x=\frac{-3 \pi}{5}\)

Not possible