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Prove that

sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA

1 answer

Use the same method as my other proof, but let
(n+1)A = x and
(n+2)A = y
y-x = A

sin(n+1)Asin(n+2)A+cos(n+1)Acos(n+2)A
= sinxsiny + cosxcosy
= cos(y-x) = cosA

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