Question

If $0\le x<\frac{\pi }{2}$ , then the number of values of $x$ for which $sinx-sin2x+sin3x=0$, is

• A. 2
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (A)

$\sin x-\sin 2x+\sin 3x=0$
$\Rightarrow \left(\sin x+\sin 3x\right)-\sin 2x=0$
$\Rightarrow 2\sin 2x.\cos x-\sin 2x=0$
$\Rightarrow \sin 2x\left(2\cos x-1\right)=0$
$\Rightarrow \sin 2x=0or\cos x=\frac{1}{2}$
$\Rightarrow x=0,\frac{\pi }{3}$