Question

Решить урравнение.
cos3xcosx=cos2x?

Answer 1

cos3x*cosx = cos2x

1/2*[cos(3x-x) + cos(3x + x)] = cos2x

cos2x - cos4x = 2 cos2x

cos4x - cos2x = 0

2*[sin(4x + 2x)/2 * sin(2x - 4x)/2] = 0

1)  sin3x = 0

3x = πn, n∈Z

x = πn/3, n∈z

2)  sinx = 0

x =  πk, k∈Z