JEE Mains · Maths · STD 11 - Trigonometrical equations
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 & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
\(\sin \,x - \sin \,2x\, + \,\sin \,3x\, = \,0\) \( \Rightarrow \,(\sin \,x + \,\sin \,3x)\, - \,\sin \,2x\, = \,0\) \( \Rightarrow \,2\,\sin x.\,\cos \,x\, - \,\sin \,2x\, = \,0\) \( \Rightarrow \,\sin \,2x\,(2\cos x\, - \,1)\, = \,0\) \( \Rightarrow \,\sin \,2x\, = \,0\) or…
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