5cos^2x-5cosx=1-3sin^2x

Question

5cos^2x-5cosx=1-3sin^2x

Answer 1

5cos^2x-5cosx=1-3sin^2x
5cos^2x-5cosx=1-3(1-cos^2x)
5cos^2x-5cosx=1-3+3cos^2x
2cos^2x-5cosx+2=0
D=25-16=9
cosx=(5+3)/4=2>1 нт
cosx=(5-3)/4=1/2
x=pi/3+2pin
x=-pi/3+2pin