Simplify (cos(theta)+cot(theta)sin(theta))/(sin(theta))

$\frac{\cos (θ) + \cot (θ) \sin (θ)}{\sin (θ)}$

Simplify the numerator.

Rewrite in terms of sines and cosines, then cancel the common factors.

Rewrite $\cot (θ) \sin (θ)$ in terms of sines and cosines.

$\frac{\cos (θ) + \frac{\cos (θ)}{\sin (θ)} \sin (θ)}{\sin (θ)}$

Cancel the common factors.

$\frac{\cos (θ) + \cos (θ)}{\sin (θ)}$

Add $\cos (θ)$ and $\cos (θ)$ .

$\frac{2 \cos (θ)}{\sin (θ)}$

Separate fractions.

$\frac{2}{1} \cdot \frac{\cos (θ)}{\sin (θ)}$

Convert from $\frac{\cos (θ)}{\sin (θ)}$ to $\cot (θ)$ .

$\frac{2}{1} \cot (θ)$

Divide $2$ by $1$ .

$2 \cot (θ)$