# Trigonometry Examples

Start on the left side.

Write in sines and cosines using the quotient identity.

Write in sines and cosines using the quotient identity.

To write as a fraction with a common denominator, multiply by .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Combine.

Reorder terms.

Combine the numerators over the common denominator.

Simplify each term.

Apply pythagorean identity.

Now consider the right side of the equation.

Apply the reciprocal identity to .

Apply the reciprocal identity to .

Multiply and to get .

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

is an identity