[tex]\frac{1}{1+cosx}+\frac{1}{1-cosx}=\frac{2}{cosx}[/tex]
Multiply by LCD(1-cos²x)(cosx)
cosx-cos²x+cosx+cos²x=2-2cos²x
Cancel the cos²x on the left
2cosx=2-2cos²x
Divide both sides by 2
cosx=1-cos²x
Transpose
cos²x+cosx-1=0
cosx=1-cos²x
cosx=sin²x
Hope this helps =)
