Question

y = cos2x - ln |cosx|

Answer 1

cos2x=sinx-cosx 

cos²x-sin²x+(cosx-sinx)=0 
(cosx-sinx)(cosx+sinx)+(cosx-sinx)=0 
(cosx-sinx)(cosx+sinx+1)=0 

cosx=sinx => x=π/4+πn 

cosx+sinx=-1 
sin(x+π/4)=-1/√2 
x+π/4=(-1)^(n+1) π/4+πk 
x=-π/4+(-1)^(n+1) π/4+πk