Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factors.

$\frac{\cos (θ) + \cos (θ)}{\cot (θ)}$

Step 1.2

Add $\cos (θ)$ and $\cos (θ)$ .

$\frac{2 \cos (θ)}{\cot (θ)}$

Step 2

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

$\frac{2 \cos (θ)}{\frac{\cos (θ)}{\sin (θ)}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$2 \cos (θ) \frac{\sin (θ)}{\cos (θ)}$

Step 4

Cancel the common factor of $\cos (θ)$ .

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Step 4.1

Factor $\cos (θ)$ out of $2 \cos (θ)$ .

$\cos (θ) \cdot 2 \frac{\sin (θ)}{\cos (θ)}$

Step 4.2

Cancel the common factor.

$\cos (θ) \cdot 2 \frac{\sin (θ)}{\cos (θ)}$

Step 4.3

Rewrite the expression.

$2 \sin (θ)$