use double angle identity:
[tex]cos (2x) = 1-2sin^2 (x)[/tex]
After substituting and moving to Right side of equation:
[tex]2 sin^2 (x) + sin (x) -1 = 0[/tex]
This is a quadratic, which can be solved by factoring or quadratic formula.
It may be helpful to replace sin(x) with another variable, then solve.
[tex]u = sin(x) \\ 2u^2 +u-1=0 \\ (2u-1)(u+1) = 0 \\ u = \frac{1}{2} , -1[/tex]
Now substitute sin(x) back in, we have
[tex]sin (x) = \frac{1}{2}, -1[/tex]
Using a unit circle or inverse sine function in calculator we can find the appropriate angles.
[tex]x = \frac{\pi}{6}, \frac{3\pi}{2}[/tex]
