Question

How do you write the product `2cos5thetasin2theta` as a sum or difference?

Answer 1

sin (7t) - sin (3t)

Explanation:

Use trig identity:
`sin x - sin y = 2cos ((x + y)/2)sin ((x - y)/2)`
In this case:
`(x + y)/2 = 5` --> x + y = 10 (1)
`(x - y)/2 = 2` --> x - y = 4 (2)
Solve (1) and (2), we get:
x = 7 and y = 3
There for,
`sin (7t) - sin (3t) = 2cos (5t).sin (2t)`