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