Trigonometry Examples

$\cos (t) \cot (t) = \frac{1 - \sin^{2} (t)}{\sin (t)}$

Step 1

Start on the right side.

$\frac{1 - \sin^{2} (t)}{\sin (t)}$

Step 2

Apply pythagorean identity.

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

Step 3

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

$\cos (t) \cot (t)$

Step 4

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

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