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

Verify the Identity sec(theta)-cos(theta)=sin(theta)tan(theta)