Sin(2x+3π/2)-sin(π/2-2x)=-√2

Question

Sin(2x+3π/2)-sin(π/2-2x)=-√2

Answer 1

-cos2x - cos2x = -√2
-2cos2x = -√2
cos2x = √2/2
2x = +-arccos(√2/2) + 2πn, n ∈ Z
2x = +-π/4 + 2πn, n ∈ Z
x = +-π/8 + πn, n ∈ Z