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Q.
What is the value of x that satisfies the equation $\cos^{-1} x = 2 \, \sin^{-1} \, x$ ?
Inverse Trigonometric Functions
Solution:
Given that $\cos^{-1} x = 2 \sin^{-1} x $
$ \Rightarrow \frac{\pi}{2} - \sin^{-1} x = 2 \sin^{-1} x $
$ \Rightarrow \frac{\pi}{2} = 3 \sin^{-1} x $
$ \Rightarrow \sin^{-1} x = \frac{\pi}{6} $
So, $ x = \sin \frac{\pi}{6} = \frac{1}{2} $