prove that tan(45+theta)+tan(45-theta)=2sec2theta

Answer 1

(1+tan x)/(1-tan x) + (1-tan x)/(1+tan x)
= [(1+tan x)^2 + (1-tan x)^2]/(1-tan^2 x)
= (2 + 2tan^2 x)/(1-tan^2 x)
= 2(cos^2 x + sin^2 x)/(cos^2 x - sin^2 x)
= 2/cos 2x
= 2sec 2x