**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 (*x* – *y*).

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(*x* – *y*) = 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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