A) 0
B) 1
C) 2
D) infinite
Correct Answer: A
Solution :
| \[(\sin x-sin3x)+2sin2x=3\] |
| \[\Rightarrow -\,2\sin x\,\cos 2x+2\,\,\sin 2x=3\] |
| \[\Rightarrow 2\sin x\cos 2x-2\sin 2x+3=0\] |
| \[2\sin x\cos 2x-2\sin \,\,2x+({{\sin }^{2}}x+{{\cos }^{2}}x)\]\[+\,\,({{\sin }^{2}}2x+{{\cos }^{2}}2x)+1=0\] |
| \[\Rightarrow {{(1-\sin 2x)}^{2}}+{{(\sin x+\cos \,2x)}^{2}}+{{\cos }^{2}}x=0\] |
| \[\Rightarrow \]No root |
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