Prove the following identity.
(Cos x + cos y)^2+ (sin x - sin y)^2 =2+2cos(x+y)

Im supposed to do it like this ( below ). I struggled with this unit of proofs so any help would be appreciated. Thanks :-)
http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/6a936af3-8727-47c8-9fbc-0a62a6770f84.gif

Question

Prove the following identity.
(Cos x + cos y)^2+ (sin x - sin y)^2 =2+2cos(x+y)

Im supposed to do it like this ( below ). I struggled with this unit of proofs so any help would be appreciated. Thanks :-)
http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/6a936af3-8727-47c8-9fbc-0a62a6770f84.gif

campbell_st · Answer

well start by expanding them

campbell_st · Answer

the expansions are 

$$(\cos(x) + \cos(y))^2 = \cos^2(x) + 2\cos(x)\cos(y) + \cos^2(y)$$

and 

$$(\sin(x) - \sin(y))^2= \sin^2(x) - 2\sin(x)\sin(y) + \sin^2(y)$$

and use a couple of basic trig identities... and see where you end up