Starting with the Pythagorean identity, sin2θ + cos2θ = 1, you can derive cotangent and cosecant Pythagorean identities. All you do is throw in a little algebra and apply the reciprocal and ratio identities and — poof! — two new identities.
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Starting with the first Pythagorean identity, sin2θ + cos2θ = 1, divide each term by sin2θ.
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Rewrite each term.
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Replace each of the terms with an equivalent expression.
Substituting these expressions into the equation and simplifying, you find that the result is
