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Q.
Number of solution of the equation $\sin ^{-1}(1-x)-4 \sin ^{-1} x=\frac{\pi}{2}$, is equal to
Inverse Trigonometric Functions
Solution:
$ \sin ^{-1}(1-x)=\frac{\pi}{2}+4 \sin ^{-1} x$
Given equation is defined if $0 \leq x \leq 1$
$\therefore$ R.H.S. $\geq \frac{\pi}{2}$, where L.H.S $\leq \frac{\pi}{2}$
$\therefore x =0$ is only solution.