Question

Number of solution of the equation $\sin ^{-1}(1-x)-4 \sin ^{-1} x=\frac{\pi}{2}$, is equal to

• A. 5
• B. 2
• C. 3
• D. 1

Answer 1

Answer: (D)

$\sin ^{-1}(1-x)=\frac{\pi}{2}+4 \sin ^{-1} x$
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.