Question

prove that tan( pie/4 + theta) + tan(5/4 - theta) = 2 sec 2 theta​

Answer 1

hey mate here is your answer

tan(pi/4 + x) + tan(pi/4 - x) =

(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(1+tan^2 x)/(1-tan^2 x)

=2(cos^2 x+sin^2 x)/(cos^2x-sin^2 x)

= 2/cos2x = 2sec2x

hope it's help you :)