In this video I derive addition and subtraction identities, cos(x+y) and cos(x-y), using the Law of Cosines and the Pythagorean Theorem. This identity is very useful in all of mathematics and is used in the derivations of many trigonometric derivatives and integrals.
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Cosine Addition and Subtraction Formulas
Subtraction: cos(x-y) = cos(x)cos(y) + sin(x)sin(y)
Addition: cos(x+y) = cos(x)cos(y) - sin(x)sin(y)
Combining Addition and Subtraction Formulas