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Number of solutions of equation 2"sin" x...

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

Text Solution

Verified by Experts

The correct Answer is:
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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