Simplify 3tan(x)cos(x)cot(x)

$3 \tan (x) \cos (x) \cot (x)$

Step 1

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

Add parentheses.

$3 (\tan (x) \cos (x)) \cot (x)$

Rewrite $3 \tan (x) \cos (x)$ in terms of sines and cosines.

$3 (\frac{\sin (x)}{\cos (x)} \cos (x)) \cot (x)$

Cancel the common factors.

$3 \sin (x) \cot (x)$

Step 2

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

Add parentheses.

$3 (\sin (x) \cot (x))$

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

$3 (\cot (x) \sin (x))$

Rewrite $3 \sin (x) \cot (x)$ in terms of sines and cosines.

$3 (\frac{\cos (x)}{\sin (x)} \sin (x))$

Cancel the common factors.

$3 \cos (x)$