# Trigonometry Examples

Verify the Identity sec(x)-cos(x)=sin(x)tan(x)
Start on the left side.
Apply the reciprocal identity to .
Write as a fraction with denominator .
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.
Multiply by .
Combine the numerators over the common denominator.
Multiply .
Apply pythagorean identity.
Now consider the right side of the equation.
Write in sines and cosines using the quotient identity.
Multiply .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity