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.
Sorry Soroban, I completely disagree. While it is more elegant to start with one side and go through logical steps to get to the other, it is still perfectly valid to prove the truth of an identity by working with both sides of an equation and showing that they are equivalent to the same thing. The transitive property states that if two things are equal to the same thing, then they are equal to each other.