## The Addition Formulas The fundamental identities are very important for the analysis of trigonometric expressions and functions but they are a direct result of the intimate relation between trigonometry and geometry. The power behind the algebraic nature of trigonometry is hidden and can be measured only with the addition formulas and Of course, we used the fact that Example. verify the identity  which gives But and since and , we get finally Remark. In general it is good to check whether the given formula is correct. One way to do that is to substitute some numbers for the variables. For example, if we take a=b = 0, we get or we may take . In this case we have Example. Find the exact value of  Hence, using the additions formulas for the cosine function we get Since we get Example. Find the exact value for  Since we get Finally we have Remark. Using the addition formulas, we generate the following identities More identities may be proved similar to the above ones. The bottom line is to remember the addition formulas and use them whenever needed. [Trigonometry]
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Tue Dec 3 17:39:00 MST 1996