Trigonometry Examples

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\cos (x)} = \tan (x) \csc (x)$

Step 1

Start on the left side.

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\cos (x)}$

Step 2

Apply pythagorean identity.

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

Step 3

Rewrite $\frac{1}{\cos (x)}$ as $\tan (x) \csc (x)$ .

$\tan (x) \csc (x)$

Step 4

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

$\frac{\csc^{2} (x) - \cot^{2} (x)}{\cos (x)} = \tan (x) \csc (x)$ is an identity