Решите уравнения sin 2x - cos 2x=1

Sin2x - cos2x = 1                        

a*sin(x) -b cos(x) 
√(a²+b)² = √2

√2sin(2x-π/4)=1
sin(2x-π/4) = 1/√2
2x-π/4 = (-1)^k * π/4 + πk, k ∈ Z
2x=(-1)^k * π/4 + π/4 + πk, k ∈ Z
x=(-1)^k * π/8 + π/8 + πk/2, k ∈ Z