Question

(cosx-sinx)(cosx+sinx)=cos3п/4

Answer 1

Решение
(cosx - sinx)(cosx + sinx) = cos(3π/4)
cos²x - sin²x = - √2/2
cos2x = - √2/2
2x = (+ -)arccos(-√2/2) + 2πk, k∈Z
2x = (+ -)(π - π/4) + 2πk, k∈Z
2x = (+ -)3π/4 + 2πk, k∈Z
x = (+ -)3π/8 + πk, k∈Z