Question

(cos x-√2/2)(sin x+√2/2)=0

Answer 1

(cosx - √2/2)=0, x=+-π/4 + 2πk, k∈Z
(sinx + √2/2)=0, x= -π/4 +2πk, x=-3π/4 +2πk, k∈Z
объединяем ответы, получаем
x=π/4 + πk, x= -π/4 +2πk, k∈Z