# Trigonometry Examples

Start on the right side.

Factor out of .

Factor out of .

Factor out of .

Multiply by .

Apply Pythagorean identity in reverse.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Apply Pythagorean identity in reverse.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Simplify .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Add and .

Add and .

Simplify each term.

Apply the distributive property.

Multiply by .

Simplify .

Multiply by .

Multiply by .

Remove unnecessary parentheses.

Subtract from .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Now consider the left side of the equation.

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Remove parentheses.

Simplify and combine like terms.

Because the two sides have been shown to be equivalent, the equation is an identity.

is an identity