Cos(4x-пи/4)cosx+sin(4x-пи/4)sinx=-корень из 2 /2

Question

Cos(4x-пи/4)cosx+sin(4x-пи/4)sinx=-корень из 2 /2

Answer 1

Cosacosb+sinasinb=cos(a-b)
cos(4x-π/4-x)=√2/2
cos(3x-π/4)=√2/2
3x-π/4=π/4+2πn U 3x-π/4=-π/4+2πn
3x=π/2+2πn U 3x=2πn
x=π/6+2πn/3 U x=2πn/3