Trigonometry Examples

$\tan (- x) \cdot \cos (x) = - \sin (x)$

Start on the left side.

$\tan (- x) \cdot \cos (x)$

Since $\tan (- x)$ is an odd function, rewrite $\tan (- x)$ as $- \tan (x)$ .

$- \tan (x) \cdot \cos (x)$

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

$- \frac{\sin (x)}{\cos (x)} \cdot \cos (x)$

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

$- \sin (x)$

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

$\tan (- x) \cdot \cos (x) = - \sin (x)$ is an identity