Algebra Examples

$\frac{\cot (x) + 2 \cos (x)}{\csc (x) - \sin (x)}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{\frac{\cos (x)}{\sin (x)} + 2 \cos (x)}{\csc (x) - \sin (x)}$

Step 1.2

Factor $\cos (x)$ out of $\frac{\cos (x)}{\sin (x)} + 2 \cos (x)$ .

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Step 1.2.1

Factor $\cos (x)$ out of $\frac{\cos (x)}{\sin (x)}$ .

$\frac{\cos (x) \frac{1}{\sin (x)} + 2 \cos (x)}{\csc (x) - \sin (x)}$

Step 1.2.2

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

$\frac{\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2}{\csc (x) - \sin (x)}$

Step 1.2.3

Factor $\cos (x)$ out of $\cos (x) \frac{1}{\sin (x)} + \cos (x) \cdot 2$ .

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\csc (x) - \sin (x)}$

Step 2

Rewrite $\csc (x)$ in terms of sines and cosines.

$\frac{\cos (x) (\frac{1}{\sin (x)} + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Step 3

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{\cos (x) (\csc (x) + 2)}{\frac{1}{\sin (x)} - \sin (x)}$

Step 4

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$\frac{\cos (x) (\csc (x) + 2)}{\csc (x) - \sin (x)}$