Question

Express the given product as a sum or difference containing only sines or cosines:
cos(2x)cos(5x)

Answer 1

what do you want to do with this?

Answer 2

express the given product as a sum or difference containing only sines or cosines

Answer 3

you can use the identity

cos u + cos v = 2 cos[ (u+v)/ 2 ]*cos [(u - v)/2]

Answer 4

here here (u+v)/2 = 5 and (u-v)/2 = 2
solving for u and v we have u = 7 and v = 3

so 2 cos 5x cos 2x = cos 7x + cos 3x

cos 5x cos 2x = 0.5cos 7x + 0.5 cos 3x