Product to Sum and Sum to Product Formulas
SumProduct Identities 




Alternate forms of the sumproduct identities are the productsum identities.
ProductSum Identities 




Example 1: Express the product cos(3x)sin(2x) as a sum of trigonometric functions.
Step 1: Notice that the problem is the product of cosine and sine, therefore use the product sum identity
Step 2: Using substitution let x = 3x and y = 2x
Step 3: Simplify
Example 2: Express the sum cos(5x) + cos(7x) as a product trigonometric functions
Step 1: Notice that it is a sum of cosine and cosine, therefore use the sumproduct identity:
Step 2: Using substitution let x = 5x and y = 7x
Step 3: Simplify
Step 4: Use the even/odd function rule cos(x) = cos (x) to replace with
Example 3: Find the exact value of sin 75° + sin 15°.
Step 1: Notice that it is a sum of sine and sine, therefore use the sumproduct identity:
Step 2: Using substitution let x = 75 and y = 15
Step 3: Simplify
Step 4: Substitute the familiar values of sin 45 = and cos 30 = into the equation and simplify
Using the sumproduct and the product sum identities can make it easier to rewrite trigonometric identities in order to evaluate functions.
Related Links: Math Trigonometry Double Angle Identities Half Angle formulas 
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