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Question

$\sin \,x - \sin \,2x\, + \,\sin \,3x\, = \,0$

$ \Rightarrow \,(\sin \,x + \,\sin \,3x)\, - \,\sin \,2x\, = \,0$

$ \Rightarrow \,2\,\sin x.\,\co

Vedclass · Accepted Answer

$2$

Vedclass · Answer

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

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

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