# Trigonometry Examples

Step 1

Multiply the numerator and denominator of by the conjugate of to make the denominator real.

Step 2

Step 2.1

Combine.

Step 2.2

Simplify the numerator.

Step 2.2.1

Apply the distributive property.

Step 2.2.2

Multiply by .

Step 2.2.3

Multiply by .

Step 2.3

Simplify the denominator.

Step 2.3.1

Expand using the FOIL Method.

Step 2.3.1.1

Apply the distributive property.

Step 2.3.1.2

Apply the distributive property.

Step 2.3.1.3

Apply the distributive property.

Step 2.3.2

Simplify.

Step 2.3.2.1

Multiply by .

Step 2.3.2.2

Multiply by .

Step 2.3.2.3

Multiply by .

Step 2.3.2.4

Multiply by .

Step 2.3.2.5

Raise to the power of .

Step 2.3.2.6

Raise to the power of .

Step 2.3.2.7

Use the power rule to combine exponents.

Step 2.3.2.8

Add and .

Step 2.3.2.9

Add and .

Step 2.3.2.10

Add and .

Step 2.3.3

Simplify each term.

Step 2.3.3.1

Rewrite as .

Step 2.3.3.2

Multiply by .

Step 2.3.4

Add and .

Step 3

Step 3.1

Factor out of .

Step 3.2

Factor out of .

Step 3.3

Factor out of .

Step 3.4

Cancel the common factors.

Step 3.4.1

Factor out of .

Step 3.4.2

Cancel the common factor.

Step 3.4.3

Rewrite the expression.

Step 4

Split the fraction into two fractions.

Step 5

Move the negative in front of the fraction.