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

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  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

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