Simplify cot(theta)sin(theta)cos(theta)

$\cot (θ) \sin (θ) \cos (θ)$

Step 1

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

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

$\frac{\cos (θ)}{\sin (θ)} \sin (θ) \cos (θ)$

Cancel the common factors.

$\cos (θ) \cos (θ)$

Step 2

Multiply $\cos (θ) \cos (θ)$ .

Raise $\cos (θ)$ to the power of $1$ .

$\cos^{1} (θ) \cos (θ)$

Raise $\cos (θ)$ to the power of $1$ .

$\cos^{1} (θ) \cos^{1} (θ)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${\cos (θ)}^{1 + 1}$

Add $1$ and $1$ .

$\cos^{2} (θ)$