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

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(B)-cos(B)=sin(B)tan(B)

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