Find the Exact Value sin(theta)+cos(theta)*cot(theta)

$\sin (θ) + \cos (θ) \cdot \cot (θ)$

Step 1

Simplify each term.

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

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

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

Raise $\cos (θ)$ to the power of $1$ .

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

Raise $\cos (θ)$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $1$ .

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

Step 2

Simplify each term.

Factor $\cos (θ)$ out of $\cos^{2} (θ)$ .

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

Separate fractions.

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

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

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

Divide $\cos (θ)$ by $1$ .

$\sin (θ) + \cos (θ) \cot (θ)$