SOLUTION: Prove that sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA

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Question 551032: Prove that
sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sin[(n+1)A]sin[(n+2)A] + cos[(n+1)A]cos[(n+2)A] = cosA

Use the commutative principles of multiplication and addition
to rearrange the left side as

cos[(n+2)A]cos[(n+1)A] + sin[(n+2)A]sin[(n+1)A]

The left side is the right side of the identity 
                cos%28alpha-beta%29=cos%28alpha%29cos%28beta%29%2Bsin%28alpha%29sin%28beta%29 with alpha=%28n%2B2%29A and beta=%28n%2B1%29A

So the left side becomes:

cos[(n+2)A - (n+1)A]

cos[nA + 2A - nA - A]

cos(A)

Edwin