# Verify the Identity sec(x)-tan(x)sin(x)=cos(x)

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