Reciprocal identities
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Pythagorean Identities
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Quotient Identities
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Co-Function Identities
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Even-Odd Identities
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Sum-Difference Formulas
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Double Angle Formulas
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Power-Reducing/Half Angle Formulas
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Sum-to-Product Formulas
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Product-to-Sum Formulas
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Numbers... one mistake is all it takes to screw the whole thing up.