Trigonometry Examples

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

Step 1

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

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

Step 2

Rewrite in terms of sines and cosines, then cancel the common factors.

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Step 2.1

Reorder $\sin (x)$ and $- \cot (x)$ .

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

Step 2.2

Add parentheses.

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

Step 2.3

Rewrite $\sin (x) \cdot (- \cot (x))$ in terms of sines and cosines.

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

Step 2.4

Cancel the common factors.

$- \cos (x)$