Question

How do you use the product to sum formulas to write `3sin2alphasin3alpha` as a sum or difference?

Answer 1

`3/2[cos a - 1/2cos 5a]`

Explanation:

Use trig identity (product to sum):
`sin x.sin y = 1/2[cos (x - y)- (1/2)cos (x + y)]`
In this case:
x = 2a and y = 3a
x - y = a, and (x + y) = 5a
We get:
`3sin 2a.sin 3a = (3/2)[cos a - (1/2)cos 5a]`