Question

The number of solutions of $\sin x=\sin 2x$ between $\frac{-\pi }{2}$ and $\frac{\pi }{2}$ is

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

Answer: (A)

Given, $\sin x=\sin 2x$
$\Rightarrow$ $\sin x=2\sin x\cos x$
$\Rightarrow$ $\sin x(1-2\cos x)=0$
$\Rightarrow$ $\sin x=0$ or $\cos x=\frac{1}{2}$
$\Rightarrow$ $x=0^o$ or $x={60}^{o,}-{60}^o$
Hence, number of solution is 3.