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Sum and Difference Formulas for Sine and Cosine

Expanding things like sin (x + y)

7.34    Apply an identity to express both of the following expressions as a sum of two products: sin (x + y) and sin (xy).

Sum and difference identities allow you to rewrite a trigonometric statement whose argument is a sum or a difference. The result is usually not simpler; you transform a single trigonometric statement into a sum or difference of two products. Though these identities do not necessarily simplify an expression, they are no less important.

The argument of sin (x + y) is (x + y).

sin (x + y) = sin x cos y + cos x sin y              sin(xy) = sin x cos y – cos x sin y

Notice that the left-hand formula above contains addition signs on both sides ...

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