Precalculus Examples

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

Step 1

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

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

Step 2

To write $\cot (x)$ as a fraction with a common denominator, multiply by $\frac{1 + \cos (x)}{1 + \cos (x)}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{\sin (x) + \cot (x) \cdot 1 + \cot (x) \cos (x)}{1 + \cos (x)} + 1$

Step 4.2

Multiply $\cot (x)$ by $1$ .

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