sec2A + tan2A ≡ tan(45 + A)?

Sol
Tan(45度+A)－Tan(2A)
=(Tan45度+TanA)/(1－Tan45度TanA)－2TanA/(1－Tan^2 A)
=(1+TanA)/(1－TanA)－2TanA/(1－Tan^2 A)
=(1+TanA)^2/(1－Tan^2 A)－2TanA/(1－Tan^2 A)
=(1+Tan^2 A)^2/(1－Tan^2 A)
=Cos^2 A(1+Tan^2 A)^2/[Cos^2 A(1－Tan^2 A)]
=(Cos^2 a+Sin^2 A)^2/(Cos^2 A－Sin^2 A)
=1/Cos(2A)
=Sec(2A)