Simplify cot(theta)+1/(tan(theta))+(cos(theta))/(sin(theta))

$\cot (θ) + \frac{1}{\tan (θ)} + \frac{\cos (θ)}{\sin (θ)}$

Simplify each term.

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

$\frac{\cos (θ)}{\sin (θ)} + \frac{1}{\tan (θ)} + \frac{\cos (θ)}{\sin (θ)}$

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

$\frac{\cos (θ)}{\sin (θ)} + \frac{1}{\frac{\sin (θ)}{\cos (θ)}} + \frac{\cos (θ)}{\sin (θ)}$

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (θ)}{\cos (θ)}$ .

$\frac{\cos (θ)}{\sin (θ)} + 1 \frac{\cos (θ)}{\sin (θ)} + \frac{\cos (θ)}{\sin (θ)}$

Write $1$ as a fraction with denominator $1$ .

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

Simplify.

Rewrite the expression.

$\frac{\cos (θ)}{\sin (θ)} + 1 \frac{\cos (θ)}{\sin (θ)} + \frac{\cos (θ)}{\sin (θ)}$

Multiply $\frac{\cos (θ)}{\sin (θ)}$ by $1$ .

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

Simplify terms.

Combine the numerators over the common denominator.

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

Add $\cos (θ)$ and $\cos (θ)$ .

$\frac{2 \cos (θ) + \cos (θ)}{\sin (θ)}$

Add $2 \cos (θ)$ and $\cos (θ)$ .

$\frac{3 \cos (θ)}{\sin (θ)}$

Separate fractions.

$\frac{3}{1} \cdot \frac{\cos (θ)}{\sin (θ)}$

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

$\frac{3}{1} \cot (θ)$

Divide $3$ by $1$ .

$3 \cot (θ)$