Trigonometry Examples

$\csc (x) \cdot \cos (x) = \cot (x)$

Step 1

Start on the left side.

$\csc (x) \cdot \cos (x)$

Step 2

Apply the reciprocal identity to

$\csc (x)$ .

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

Step 3

Combine

$\frac{1}{\sin (x)}$ and

$\cos (x)$ .

$\frac{\cos (x)}{\sin (x)}$

Step 4

Rewrite

$\frac{\cos (x)}{\sin (x)}$ as

$\cot (x)$ .

$\cot (x)$

Step 5

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

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