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Question

The number of solution of equation 2 sin 2x+sin x(12 cos 2x)4=0 in the interval (0,π) is -

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Solution

4 sin x cos x+sin x(12(2 cos2 x1))=4

4 cos x+14 cos2 x+2=4sin x

4(2 cos x1)2=4sin x

L.H.S4 and R.H.S4 and equality holds when cos x=12 and sin x=1 which is not possible.

Hence, no solution.

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