Trigonometry Examples

$(1 - \sin^{2} (x)) \csc (x) = \cos (x) \cot (x)$

Step 1

Start on the left side.

$(1 - \sin^{2} (x)) \csc (x)$

Step 2

Apply pythagorean identity.

$\cos^{2} (x) \csc (x)$

Step 3

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

$\cos^{2} (x) \frac{1}{\sin (x)}$

Step 4

Combine ${\cos (x)}^{2}$ and $\frac{1}{\sin (x)}$ .

$\frac{\cos^{2} (x)}{\sin (x)}$

Step 5

Rewrite $\frac{\cos^{2} (x)}{\sin (x)}$ as $\cos (x) \cot (x)$ .

$\cos (x) \cot (x)$

Step 6

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

$(1 - \sin^{2} (x)) \csc (x) = \cos (x) \cot (x)$ is an identity