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Number of solutions of equation `2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(2) x=cos^(2) x-sin^(2) x` for `x in [0, 4pi]` is

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Number of solutions of equation `2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(2) x=cos^(2) x-sin^(2) x` for `x in [0, 4pi]` is
A. 6
B. 8
C. 10
D. 12
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Correct Answer - C
`(cos^(2) x-sin^(2) x) (2 "sin" x/2-1)=0`
`cos 2x=0 or "sin" x/2=1/2`
`:.` Number of solution `=8+2=10`
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