Question

If $0 \le x < \frac{\pi}{2}$ , then the number of values of $ x$ for which $sin \,x-sin\,2x+sin\,3x = 0$, is

• A. 2
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (A)

$\sin x -\sin2x+\sin3x =0$
$ \Rightarrow \left(\sin x + \sin3x\right) -\sin2x =0$
$ \Rightarrow 2\sin 2x. \cos x- \sin2x =0$
$ \Rightarrow \sin2x \left(2 \cos x-1\right)=0 $
$ \Rightarrow \sin2x = 0 or \cos x = \frac{1}{2}$
$ \Rightarrow x = 0, \frac{\pi}{3} $