Please type this as 2(sin 2x)^2=2 2sin^2 2x=2 is confusing.
Reducing this expression: (sin 2x)^2 = 1
Taking the sqrt of both sides, sin 2x = plus or minus 1
If sin 2x = 1, then 2x must be pi/2 or 3pi/2, and so x must be pi/4 or 3pi/4.
Now you do this for sin 2x = -1.
