Trigonometry Examples

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

Step 1

Start on the right side.

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

Step 2

Apply pythagorean identity.

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

Step 3

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

$\sin (t) \tan (t)$

Step 4

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

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