Решить уравнение1 + 2cos3xcosx - cos2x = 0

Question

Решить уравнение
1 + 2cos3xcosx - cos2x = 0

Answer 1

1 + 2cos3xcosx - cos2x = 0

2cos3xcosx = 2(cos(3x+x) +cos(3x-x))/2= cos4x+cos2x

1+cos4x+cos2x-cos2x=0

1+cos4x=0

cos4x=-1

4x = пи +2пи*n

x =пи/4+ (пи/2)*n