Trigonometric equation

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2sin x.sin 3x-cos 2x=0

[shyamjayakannan]

[tex]2\sin x\sin{3x}-\cos{2x}=0\Rightarrow2\sin x(\sin x\cos{2x}+\cos x\sin{2x})-\cos{2x}=0\Rightarrow2\sin^2x\cos{2x}+2\sin x\cos x\sin{2x}-\cos{2x}=0[/tex]
[tex]\Rightarrow\cos{2x}\left(2\sin^2x-1\right)+2\sin x\cos x\sin{2x}=0\Rightarrow\cos{2x}\left(\sin^2x-\cos^2x\right)+\sin^2{2x}=0\Rightarrow-\cos^2{2x}+\sin^2{2x}=0\Rightarrow\cos{4x}=0[/tex]

Now, you can find the solution from here.