Algebra Examples

$\frac{1}{\sin (θ)} - \frac{\sin^{2} (θ)}{\sin (θ)}$

Step 1

Combine the numerators over the common denominator.

$\frac{1 - \sin^{2} (θ)}{\sin (θ)}$

Step 2

Apply pythagorean identity.

$\frac{\cos^{2} (θ)}{\sin (θ)}$

Step 3

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

$\frac{\cos (θ) \cos (θ)}{\sin (θ)}$

Step 4

Separate fractions.

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

Step 5

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

$\frac{\cos (θ)}{1} \cot (θ)$

Step 6

Divide $\cos (θ)$ by $1$ .

$\cos (θ) \cot (θ)$