Математика ЕГЭ задание 13 Cos2x-√2×sin(3π/2−x)−1=0

Question

Математика ЕГЭ задание 13
Cos2x-√2×sin(3π/2−x)−1=0

Answer 1

1-2cos²x+√2cosx-1=0
-2cos²x+√2cosx=0
-√2cosx(√2cosx-1)=0
cosx=0⇒x=π/2+πn,n∈z
cosx=1/√2⇒x=+-π/4+2πk,k∈z