Question

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

Answer 1

Correct Answer - 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. "`