This is not a valid identity.

Perhaps you mean:

\frac{sin(x)+1}{cos(x)+cot(x)}=tan(x)

This is a valid identity. Convert the cot(x) to \frac{cos(x)}{sin(x)}.

\frac{sin(x)+1}{cos(x)+\frac{cos(x)}{sin(x)}}

Cross multiply the denominator, factor out a cos(x), cancel the resulting sin(x)+1 in the denominator with the one in the numerator, you will see a \frac{1}{\frac{cos(x)}{sin(x)}}. Which equals \frac{sin(x)}{cos(x)}=tan(x)