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 $0\le x\le 1$
$\therefore$ R.H.S. $\ge \frac{\pi }{2}$, where L.H.S $\le \frac{\pi }{2}$
$\therefore x=0$ is only solution.