Question

I have these sum and product property problems and I just want to make sure my work is right.

Write equations expressing
1. cos 37degrees cos99degrees as a sum
Answer: sin136+(-62)
2. sin4+sin7 as a product
Answer: 2sin5.5 sin-1.5
3. cos 8x - cos 2x as a product
Answer -2sin5x sin3x
4. cos5x sin9x as a sum
Answer sin14x - (-4)

Idk...I just don't feel as confident about these

Answer 1

recall that

cosa * cosb = 1/2[cos(a+b) + cos(a-b)]

cos37 cos99 = 1/2(cos126 + cos(-62))
= 1/2 (cos126 + cos62)
since cos(-a) = cos(a)

So, your answers have the right number sin them, but you need to tidy them up to conform to the identities.