Sin2x+корень из 2*sinx=2cosx+корень из 2

[от пи, до 5 пи/2]

2Sin x Cos x + √2 Sin x - 2 Cos x - √2 = 0

Sin x (2Cos x + √2) - (2Cos x + √2) = 0

(2Cos x + √2) (Sin x - 1) = 0

2Cos x + √2 = 0 или Sin x - 1 = 0

2Cos x = - √2 Sin x = 1

Cos x = - √2/2 x = π/2 + 2πn, n∈Z

x = + - arcCos (-√2/2) + 2πк, к∈Z

x = + - 3π/4 + 2πk, k∈Z