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The number of solutions for 2sin^(2)x+s...

The number of solutions for `2sin^(2)x+sin^(2)2x=2` when `-piltxltpi`, is

A

4

B

2

C

6

D

13

Text Solution

Verified by Experts

The correct Answer is:
C
We have , `2sin^(2)x+sin^(2)2x=2`
`rArr1-cos2x+1-cos^(2)2x=2`
`rArrcos2x+cos^(2)2x=0`
`rArrcos2x(1+cos2x)=0`
`rArrcos2x=0,cos2x=-1`
`rArrx=+-(pi)/(4),+-(3pi)/(4)`,
`x=+-(pi)/(4),+-(3pi)/(4),+-(pi)/(2)`
Thus ,there are six solutions
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