Question

How do you use the product to sum formulas to write `cos4thetasin6theta` as a sum or difference?

Answer 1

`(1/2)[sin 10t - sin (-2t)]`

Explanation:

Use trig identity:
`sin x - sin y = 2cos ((x + y)/2)sin ((x - y)/2)`
In this case:
(x + y)/2 = 4t --> x + y = 8t
(x - y)/2 = 6t --> x - y = 12t
After solving, we get:
x = 10t and y = - 2t
Finally,
`(1/2)[sin (10t) - sin (-2t] = cos 4t.sin 6t`