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If thetain(0,2pi) then number of solutio...

If `thetain(0,2pi)` then number of solution of equation
`(sin^(2)2theta+4sin^(4)theta-4sin^(2)thetacos^(2)theta)/(4-sin^(2)2theta-4sin^(2)theta)=(1)/(9)," is//are"`

A

2

B

3

C

4

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
`(sin^(2)2theta+4sin ^(4)theta-4sin^(2)thetacos^(2)theta)/(4-sin^(2)2theta-4sin^(2)theta)=(1)/(9)`
`(4sin^(4)theta)/(4cos^(2)theta-4sin^(2)thetacos^(2)theta)=(1)/(9)`
`(sin^(4)theta)/(cos^(4)theta)=(1)/(9)impliestan^(2)theta=(1)/(3)tantheta=+-(1)/(sqrt(3)):.4" solutions. "`
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