Start on the left side.

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)-sin(x)tan(x)=cos(x)