u have got the result (1+sin x)/cos x=1/cos x+sin x/cos x=sec x+tan x
tan (x/2 + Π/4) = sec x + tan x
Here is my attempt:
Substituting 1 for tan (Π/4) and applying the tangent of a sum identity gives
[tan (x/2) +1] / [1-tan(x/2)] = 1/cos x + sin x/cos x
Using the half angle identity for tangent, tan(x/2) = sin x /(1 + cos x) and simplifying the complex fraction gives
(sin x + 1 + cos x) / (1 + cos x - sin x) = (1 + sin x) / cos x
I do not know where to go from here. Please help!
(1 + sin x )/cos x was just me changing the right side, sec x + tan x, in terms of cosine and sine. I'm trying to figure out how to get the left side of the equation (sin x + 1 + cos x) / (1 + cos x - sin x) to equal (1 + sin x )/cos x. I cannot find that relationship.