**4.6 Sum and Difference Formulas**

**INTRODUCTION** In this section we continue our examination of trigonometric identities. But this time we are going to develop only those identities that are of particular importance in courses in mathematics and science.

▯ **Sum and Difference Formulas** The **sum** and **difference formulas** for the cosine and sine functions are identities that reduce cos(*x*_{1} + *x*_{2}), cos(*x*_{1} − *x*_{2}), sin(*x*_{1} + *x*_{2}), and sin(*x*_{1} − *x*_{2}) to expressions that involve cos *x*_{1}, cos *x*_{2}, sin *x*_{1}, and sin *x*_{2}. We will derive the formula for cos (*x*_{1} − *x*_{2}) first, and then we will use that result to obtain the others.

For convenience, let us suppose that *x*_{1} and *x*_{2} represent angles measured in radians. As shown in FIGURE 4.6.1(a), let *d* denote the distance between ...

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