√2/2sin x-√2/2cos x=1 Решите оч срочно плиз

Question

√2/2sin x-√2/2cos x=1 Решите оч срочно плиз

Answer 1

√2/2sinx - √2/2cosx = 1
sinxcos(π/4) - cosxsin(π/4)= 1
sin(x - π/4) = 1
x - π/4 = π/2 + 2πn, n ∈ Z
x = 3π/4 + 2πn, n ∈ Z.