# Trigonometry Examples

Start on the left side.
Convert to sines and cosines.
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 the factors of .
Combine the numerators over the common denominator.
Simplify each term.
Apply pythagorean identity.
Now consider the right side of the equation.
Convert to sines and cosines.
Apply the reciprocal identity to .
Apply the reciprocal identity to .
Multiply and .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity