Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

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

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

Step 1.1.2

Cancel the common factors.

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

Step 1.2

Add $\cos (θ)$ and $\cos (θ)$ .

$\frac{2 \cos (θ)}{\sin (θ)}$

Step 2

Separate fractions.

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

Step 3

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

$\frac{2}{1} \cot (θ)$

Step 4

Divide $2$ by $1$ .

$2 \cot (θ)$