Trigonometry Examples

$7 \sin (x) \cot (- x)$

Step 1

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

$7 \sin (x) (- \cot (x))$

Step 2

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

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Step 2.1

Add parentheses.

$7 (\sin (x) (- \cot (x)))$

Step 2.2

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

$7 (- \cot (x) \sin (x))$

Step 2.3

Add parentheses.

$7 (- (\cot (x) \sin (x)))$

Step 2.4

Rewrite $7 \sin (x) (- \cot (x))$ in terms of sines and cosines.

$7 (- (\frac{\cos (x)}{\sin (x)} \sin (x)))$

Step 2.5

Cancel the common factors.

$7 (- \cos (x))$

Step 3

Multiply $- 1$ by $7$ .

$- 7 \cos (x)$