Please help me verify this identity? tan(x + pi/4) = (cosx + sinx)/(cosx - sinx)?

We have to prove that tan(x + pi/4) = (cos x + sin x)/(cos
x - sin x)

We know that tan (a + b) = [tan a + tan b]/(1 -
tan a * tan b)

tan(x +
pi/4)

=> (tan x + tan pi/4) / (1 - tan x * tan
pi/4)

tan pi/4 = 1

=>
(tan x + 1) / ( 1 - tan x)

=> [(sin x / cos x) +
1]/[1 - (sin x / cos x)]

=> [(sin x + cos x)/cos x]/
[(cos x - sin x)/cos x]

=> (sin x + cos x)/ (cos x -
sin x)

This proves that tan(x + pi/4)= (cos x
+ sin x)/(cos x - sin x)