# How to show $\frac {\cos(x)+\sin(x)}{\cos(x)-\sin(x)}=\frac{1+\tan(x)}{1-\tan(x)}$

A step in trig expression simplification, from a textbook:

$$\frac {\cos(x)+\sin(x)}{\cos(x)-\sin(x)}\to\frac{1+\tan(x)}{1-\tan(x)}$$

Please give a hint as to how this transformation was achieved.

Divide the numerator and denominator by $\cos x$.
• And if $\cos(x) = 0$? – Henno Brandsma Oct 28 '14 at 18:50
• @HennoBrandsma if $cos(x) = 0$, then $tan(x)$ is undefined, so we can divide by $cos(x)$ because $cos(x) \ne 0$ for the identity. – Justin Oct 28 '14 at 18:51
• The left hand side is defined for those $x$, the right hand side isn't. So the equality is not quite for all $x$ then. – Henno Brandsma Oct 28 '14 at 18:54