2cos^2x-cos^2(pi/2-x)=1

Question

2cos^2x-cos^2(pi/2-x)=1

Answer 1

2cos^2x-cos^2(pi/2-x)=1
2cos^2(x) -sin^2(x)-1=0
2cos^2(x)-1+cos^2(x)-1=0
3cos^2(x)=2
(cosx-sqrt(2/3))(cosx+sqrt(2/3)=0
cosx=sqrt(2/3)
x=+/-arccos(sqrt(2/3))+2pik, k ∈Z
cosx=-sqrt(2/3)
x=+/-(pi-arccos(sqrt(2/3))+2pik, k ∈Z