Product Sum and Sum Product Formulas in Trigonometry

This is a list of the product to sum and sum to product formulas used in trigonometry.

Review

Product to Sum Formulas


  1. sin x cos y = (1/2) [ sin(x + y) + sin(x - y) ]

  2. cos x sin y = (1/2) [ sin(x + y) - sin(x - y) ]

  3. cos x cos y = (1/2) [ cos(x + y) + cos(x - y) ]

  4. sin x sin y = (1/2) [ cos(x - y) - cos(x + y) ]




Sum to Product Formulas


  1. sin x + sin y = 2*sin[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

  2. sin x - sin y = 2*cos[ (x + y) / 2 ]*sin[ (x - y) / 2 ]

  3. cos x + cos y = 2*cos[ (x + y) / 2 ]*cos[ (x - y) / 2 ]

  4. cos x - cos y = 2*sin[ (x + y) / 2 ]*sin[ (x - y) / 2 ]


More links to trigonometric formulas and identities.

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