True or false: cosu+cosv=cos(u+v), for all u and v ?

I know this relates to the sum and difference identities but I don't get the concept of how this works?

1 Answer
Nov 7, 2017

No. They are not equal.
cos(u+v) = cosu cosv - sinu sinv
cos u + cos v = 2 cos ((u+v)/2) cos ((u-v)/2)

Explanation:

cos u + cos v = cos u + cos v only and it can’t be further simplified.

It can be combined as under:

cos u + cos v = 2 cos( (u+v)/2) cos ((u-v)/2)

cos (u+v) = cos u cos v - sin u sin v