Expressing $ \frac{\cos x + \sin x}{\cos x - \sin x} $ as a single trigonometric function For a while now, I have been trying to get this expression into 1 term instead of the 2 term fraction.
$$
\frac{\cos x + \sin x}{\cos x - \sin x}
$$
The most I have gotten down to is get it to a single ratio, ie,
$$
\frac{1 + \tan x}{1 - \tan x}
$$
I have been looking for an identity or formula of some sort to factorize $ \cos x + \sin x $ and $ \cos x - \sin x $.
Any help will be appreciated.
Thanks

$
\dfrac{\cos x + \sin x}{\cos x - \sin x} = \dfrac{1+ \tan x}{1 - \tan x}
$
Now, $\tan (x+y) = \dfrac{\tan x+ \tan y}{1 - \tan x \tan y}$
Therefore,  $\tan (x+ \frac{\pi}{4}) = \dfrac{\tan x+ 1}{1 - \tan x}$
Therefore, $\dfrac{\cos x + \sin x}{\cos x - \sin x} = \tan(x+ \frac{\pi}{4})$
Is this what you meant by 1 term?.
