Trigonometry Examples

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

Step 1

Start on the left side.

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

Step 2

Apply pythagorean identity.

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

Step 3

Write $\tan (x)$ in sines and cosines using the quotient identity.

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

Step 4

Cancel the common factor of $\cos (x)$ .

$\cos (x) \sin (x)$

Step 5

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

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