you're really making this too hard ...
finish it by multiplying numerator and denominator by ...
For this question the only answer I seem to get is sinx/cosx not (sinx/(sinx+cosx))
(tanx/(1+tanx)) = (sinx/(sinx+cosx))
((1-tanx/1-tanx)) times (tanx/(1+tanx))
((tanx(1-tanx))/(1-tan^2x))
(tanx-tan^2x)/(1-tan^2x))
((cosx/cosx) times (sinx/cosx) - (sin^2x/cos^2x)) / ((cos^2x/cos^2x) times 1- (sin^2x/cos^2x))
((cosxsinx - sin^2x)/cos^2x) / ((cos^2x-sin^2x)/cos^2x)
multiply the reciprocal and cancel i get
sinx/cosx
ugh.. what did i do wrong??
Whenever you are trying to prove a trig identity with tan x, cot x, sec x or csc x, a method that usually works pretty easily is to change these into sin x and cos x and then simplify algebraically. So if you don't see a quicker way right away always try this.