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