## Product and Sum Formulas From the Addition Formulas, we derive the following trigonometric formulas (or identities) Remark. It is clear that the third formula and the fourth are equivalent (use the property to see it).

The above formulas are important whenever need rises to transform the product of sine and cosine into a sum. This is a very useful idea in techniques of integration.

Example. Express the product as a sum of trigonometric functions. which gives Note that the above formulas may be used to transform a sum into a product via the identities Example. Express as a product. Note that we used .

Example. Verify the formula  and Hence which clearly implies Example. Find the real number x such that and Answer. Many ways may be used to tackle this problem. Let us use the above formulas. We have Hence Since , the equation gives and the equation gives . Therefore, the solutions to the equation are Example. Verify the identity  Using the above formulas we get Hence which implies Since , we get  [Trigonometry]
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Tue Dec 3 17:39:00 MST 1996