Question

Cos 5x cos x=cos 2x cos 4x

Answer 1

$cos5x*cosx-cos2x*cos4x=0;\\cos3x+cos2x-cos3x-cosx=0;\\2cos^2x-cosx-1=0;D=1+8=3*3\\cosx=\frac{1б3}{4} ;\\\left[\begin{array}{ccc}cosx=1\\cosx=-\frac{1}{2}\\\end{array}$

Ответ: x={2pi*n;±2pi/3+2pi*n}, n∈Z.