Question

Express cos5mcos(-3m) as a sum or difference.

-1/2cos2m + 1/2cos2m
1/2cos2m - 1/2cos8m
1/2cos8m - 1/2cos2m
1/2cos8m + 1/2cos2m

Answer 1

D

Explanation:

Using the product to sum formula

• 2cosAcosB = cos(A+B) + cos(A - B)

note that cos(- 3m) = cos 3m, hence

cos5m cos(- 3m)

= cos 5m cos3m ← A = 5m and B = 3m

=
`(1)/(2)` ( 5m + 3m) + cos(5m - 3m) ]

=
`(1)/(2)` cos 8m +
`(1)/(2)` cos 2m