1) cos х = sin² х cos х
cosx=0 x=+-π/2+2πn
cosx≠0 sin²x=1 sinx=+-1 x=+-π/2+πn
Ответ: x=+-π/2+πn
2) 2sinx = 3sin2x
2sinx = 3*2sinx cosx
sinx = 3sinx cosx
sinx=0 x=πn
1= 3cosx cosx=1/3 x=+-arccos(1/3)+2πn
Ответ: x=πn и x=+-arccos(1/3)+2πn
3) sin 2x = sin x
2sinx cosx=sinx
sinx=0 x=πn
2cosx=1
cosx=1/2 x=+-π/3 +2πn
Ответ: x=πn и x=+-π/3 +2πn
4) cos² 4х + cos 4x = 0
cos4x(cos4x+1)=0
cos4x=0 4x=+-π/2+πn x=+-π/8+πn/4
cos4x+1=0 cos4x=-1 4x=+-πn+2πn x=+-πn/4+πn/2
Ответ: x=+-π/8+πn/4 и x=+-πn/4+πn/2