Question

Prove that

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

Answer 1

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