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

Question 551032: Prove that
sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA
Answer by Edwin McCravy(20060) (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 
                 with  and 

So the left side becomes:

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

cos[nA + 2A - nA - A]

cos(A)

Edwin

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