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Question
Prove the following:
`((1 + tan x)/(1 - tan x))^2 = tan(pi/4 + x)/(tan(pi/4 - x))`
Solution
R.H.S. = `tan(pi/4 + x)/(tan(pi/4 - x))`
= `(((tan pi/4 + tan x)/(1 - tan pi/4 tan x)))/(((tan pi/4 - tan x)/(1 + tan pi/4 tan x))) = (((1 + tanx)/(1 - (1)tan x)))/(((1 - tan x)/(1 + (1)tan x))`
= `((1 + tan x)/(1 - tan x)) xx ((1 + tan x)/(1 - tan x))`
= `((1 + tan x)/(1 - tan x))^2`
= L.H.S.
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