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)

$3$

Answer 2

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.