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 ...