Tangent and Secant Identities on a Unit Circle
Starting with the Pythagorean identity, sin2θ + cos2θ = 1, you can derive tangent and secant Pythagorean identities. All you do is throw in a little algebra and apply the reciprocal and ratio identities and — poof! — two new identities.
Starting with the first Pythagorean identity, sin2θ + cos2θ = 1, divide each term by cos2θ.
Rewrite each term.
Note how the exponent 2 is pulled out of the parentheses:
Replace each of the terms with an equivalent expression.
Substituting these expressions into the equation and simplifying, you get