Question

1 + cos 8x = 2 cos 4x;

Answer 1

Замена 4x = y, тогда cos 8x = cos 2y = 2cos^2 y - 1
1 + 2cos^2 y - 1 = 2cos y
2cos^2 y = 2cos y
2cos y*(cos y - 1) = 0
1) cos y = cos 4x = 0
4x = pi/2 + pi*k
x = pi/8 + pi/4*k
2) cos y = cos 4x = 1
4x = 2pi*k
x = pi/2*k