Tangent and Secant Identities on a Unit Circle
Starting with the Pythagorean identity, sin^{2}θ + cos^{2}θ = 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, sin^{2}θ + cos^{2}θ = 1, divide each term by cos^{2}θ.

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