prove that tan(π/4+x/2)+tan(π/4-x/2)=2sec x
tan(π/4+x/2) =
(tan π/4 + tan x/2)
-------------------------
1 - tan π/4 tan x/2
(1+tan(x/2))/(1-tan(x-2))
see where this takes you, and recall the half-angle formula for tan(x/2)
(tan π/4 + tan x/2)
-------------------------
1 - tan π/4 tan x/2
(1+tan(x/2))/(1-tan(x-2))
see where this takes you, and recall the half-angle formula for tan(x/2)