Precalculus Examples

$\csc (θ) \cdot \cos (θ) = \cot (θ)$

Step 1

Start on the left side.

$\csc (θ) \cdot \cos (θ)$

Step 2

Apply the reciprocal identity to $\csc (θ)$ .

$\frac{1}{\sin (θ)} \cdot \cos (θ)$

Step 3

Combine $\frac{1}{\sin (θ)}$ and $\cos (θ)$ .

$\frac{\cos (θ)}{\sin (θ)}$

Step 4

Rewrite $\frac{\cos (θ)}{\sin (θ)}$ as $\cot (θ)$ .

$\cot (θ)$

Step 5

Because the two sides have been shown to be equivalent, the equation is an identity.

$\csc (θ) \cdot \cos (θ) = \cot (θ)$ is an identity