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
sankarankalyanam
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#

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