Question

Prove the identity: (cos x + cos y)^2 + (sin x + sin y)^2=2+2cos(x+y)

Answer 1

expand both parentheses
(cos x +cos y)^2 = ??? )Foil)
(sin x +siny)^2 = ?

Answer 2

and after that you have to use the identity \[\rm \cos^2 \theta + \sin^2 \theta = 1\]

Answer 3

Here's how you can start it:
Break it up into familiar functions. (Cosx+Cosy)to the 2 is equavalent to
(Cosx+Cosy)(Cosx+Cosy) You foil this and end up with: Cos^2x+Cos^y+2cosxcosy
You do the same thing to the other foilable function: (Sinx+Siny)
And then solve

Answer 4

So, when I foil I do, (cos x + cos y) (cos x+ cos y) and get 4 cos x + cos(x+y) +2 cos y?

Answer 5

oh okay nevermind to what I just said lol

Answer 6

it would be easy if you draw a box like this