Trigonometry Examples

$\cot (- x) \sin (x) = - \cos (x)$

Step 1

Start on the left side.

$\cot (- x) \sin (x)$

Step 2

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

$- \cot (x) \sin (x)$

Step 3

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

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

Step 4

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

$- \cos (x)$

Step 5

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

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