Cos2x - sqrt 2 sinx=1 Find all solutions

Cos 2 x - √2 sin x = 1

cos² x - sin² x - √2 sin x = 1

1 - 2 sin² x - √2 sin x = 1

- 2 sin² x - √2 sin x = 1 - 1

- 2 sin² x - √2 sin x = 0 / · ( - 1)

2 sin² x + √2 sin x = 0

sin x (2 sin x + √2) = 0

sin x = 0, x 1 = k π, k ∈ Z

or: 2 sin x + √ 2 = 0

2 sin x = - √2

sin x = - √2 / 2

x 2 = 5 π / 4 + 2 kπ, x 3 = 7 π / 4 + 2 kπ, k ∈ Z