Question

3costheta=2sin^2theta find theta

Answer 1

3cosø = 2sin^2ø

3cosø = 2(1-cos^2ø)

3cosø = 2- 2cos^2ø

2cos^2ø + 3cosø - 2 = 0

Now it's a quadratic equation

2cos^2ø + 4cosø - cosø -2 = 0

2cosø ( cosø + 2 ) - 1 ( cosø + 2 ) = 0

( 2cosø - 1 )( cosø + 2 ) = 0

cosø = 1/2 or -2

As -2 is not possible in the cosine ratio,

cosø = 1/2

ø = 60 degrees