Trigonometry Workbook For Dummies
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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.

  1. Starting with the first Pythagorean identity, sin2θ + cos2θ = 1, divide each term by cos2θ.

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  2. Rewrite each term.

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    Note how the exponent 2 is pulled out of the parentheses:

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  3. Replace each of the terms with an equivalent expression.

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    Substituting these expressions into the equation and simplifying, you get

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About This Article

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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