15sin^2 (2x) = 1 + sin (2x)
_________ multiply both sides by 2
2
30sin^2(2x) = 1 + sin(2x) rearrange as
30sin^2(2x) - sin(2x) - 1 = 0 factor
(6 sin (2x) + 1) ( 5sin (2x) - 1) = 0
Set each factor to 0 and solve for x
6sin(2x) + 1 = 0
6sin(2x) = -1
sin(2x) = -1/6
sin(x) = -1/6 at ≈ 3.309 rads , 6.12 rads, 9.59 rads and 12.40 rads
So dividing each of these by 2 we get
x ≈ 1.6545 rads, 3.06 rads, 4.795 rads and 6.20 rads
And
5sin (2x) - 1 = 0
5sin (2x) = 1
sin(2x) = 1/5 at ≈ .201 rads, 2.94 rads, 6.48 rads, 9.22 rads
Divide both of these by 2 and we get
x ≈ .105 rads, 1.97 rads, 3.24 rads and 4.61rads
