Find all solution of cos2theta-2sintheta-1=0

express in terms of sin theta

Gonna be making theta x so it's easier to write

Since cos (2x) = 1-2sin^2x, we'll write it as that to make it 2sin^2x-2sinx+1-1=0 and 2sin^2x-2sinx=0, then making it 2 (sin^2x-sinx) = 0. After that, we make it sin^2x-sinx=0 and sin^2x=sinx, which is essentially equal when sinx=0 or sinx=1, which is pi/2 (+2pi for as long as you want) and pi (add or subtract pi as much as you want)