Cos2x-cosx=0
2cos²x-1-cosx=0
cosx=a
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-1/2⇒cosx=-1/2⇒x=+-2π/3+2πn
a2=(1+3)/4=1⇒cosx=1⇒x=2πn
x=-2π/3+2πn
n=1 x=-2π/3+2π=4π/3∈[0;5π/2]
x=2π/3+2πn
n=0 x=2π/3∈[0;5π/2]
x=2πn
n=0 x=0∈[0;5π/2]
n=1 x=2π∈[0;5π/2]
Ответ х={0;2π/3;4π/3;2π}