Proving the identity (verify) the trig function

Question

cos (x+y) + cos (x-y) = 2 cos (x) cos (y)

 

I've tried a lot of modifications to both sides but I just cannot get them to be equal

Answer 1

You need to know this basic formula: cos (x+y) = cos x cos y - sin x sin y

and also                                           cos (x-y) = cos x cos y + sin x sin y

 

and when added you get                                    2 cos x cos y    

 

DONE!