(2 cosx-3)/(2cosx-1)+1/(2cos^2x-cosx)=0

Question

(2 cosx-3)/(2cosx-1)+1/(2cos^2x-cosx)=0

Answer 1

(2 cosx-3)/(2cosx-1)+1/(2cos^2x-cosx)=0
(2 cosx-3)/(2cosx-1)+1/сosx(2cosx-1)=0
одз cosx≠0 U cosx≠1/2
2cos²x-3cosx+1=0
cosx=a
2a²-3a+1=0
D=9-8=1
a1=(3-1)/4=1/2⇒cosx=1/2∉одз
a2=(3+1)/4=1⇒cosx=1⇒x=2πn