Algebra Examples

$\frac{\cot (θ + π) \cos (θ)}{\csc (θ + 2 π)}$

Step 1

Separate fractions.

$\frac{\cos (θ)}{1} \cdot \frac{\cot (θ + π)}{\csc (θ + 2 π)}$

Step 2

Rewrite $\csc (θ + 2 π)$ in terms of sines and cosines.

$\frac{\cos (θ)}{1} \cdot \frac{\cot (θ + π)}{\frac{1}{\sin (θ + 2 π)}}$

Step 3

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

$\frac{\cos (θ)}{1} \cdot \frac{\frac{\cos (θ + π)}{\sin (θ + π)}}{\frac{1}{\sin (θ + 2 π)}}$

Step 4

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (θ + 2 π)}$ .

$\frac{\cos (θ)}{1} (\frac{\cos (θ + π)}{\sin (θ + π)} \sin (θ + 2 π))$

Step 5

Write $\sin (θ + 2 π)$ as a fraction with denominator $1$ .

$\frac{\cos (θ)}{1} (\frac{\cos (θ + π)}{\sin (θ + π)} \cdot \frac{\sin (θ + 2 π)}{1})$

Step 6

Simplify.

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Step 6.1

Divide $\sin (θ + 2 π)$ by $1$ .

$\frac{\cos (θ)}{1} (\frac{\cos (θ + π)}{\sin (θ + π)} \sin (θ + 2 π))$

Step 6.2

Combine $\frac{\cos (θ + π)}{\sin (θ + π)}$ and $\sin (θ + 2 π)$ .

$\frac{\cos (θ)}{1} \cdot \frac{\cos (θ + π) \sin (θ + 2 π)}{\sin (θ + π)}$

Step 7

Divide $\cos (θ)$ by $1$ .

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

Step 8

Combine $\cos (θ)$ and $\frac{\cos (θ + π) \sin (θ + 2 π)}{\sin (θ + π)}$ .

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

Step 9

Separate fractions.

$\frac{\cos (θ + π) \sin (θ + 2 π)}{1} \cdot \frac{\cos (θ)}{\sin (θ + π)}$

Step 10

Rewrite $\frac{\cos (θ)}{\sin (θ + π)}$ as a product.

$\frac{\cos (θ + π) \sin (θ + 2 π)}{1} (\cos (θ) \frac{1}{\sin (θ + π)})$

Step 11

Write $\cos (θ)$ as a fraction with denominator $1$ .

$\frac{\cos (θ + π) \sin (θ + 2 π)}{1} (\frac{\cos (θ)}{1} \cdot \frac{1}{\sin (θ + π)})$

Step 12

Simplify.

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Step 12.1

Divide $\cos (θ)$ by $1$ .

$\frac{\cos (θ + π) \sin (θ + 2 π)}{1} (\cos (θ) \frac{1}{\sin (θ + π)})$

Step 12.2

Convert from $\frac{1}{\sin (θ + π)}$ to $\csc (θ + π)$ .

$\frac{\cos (θ + π) \sin (θ + 2 π)}{1} (\cos (θ) \csc (θ + π))$

Step 13

Divide $\cos (θ + π) \sin (θ + 2 π)$ by $1$ .

$\cos (θ + π) \sin (θ + 2 π) \cos (θ) \csc (θ + π)$