Question

tan(45° + theta) + tan(45° - theta) = 2 sec 2theta
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Answer 1

$\huge\red{\underline{✪Answer}}$

(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

Answer 2

༄❁❁❁❁❁༄

(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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