Trigonometry
posted by Kewal .
Prove that
sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA

Use the same method as my other proof, but let
(n+1)A = x and
(n+2)A = y
yx = A
sin(n+1)Asin(n+2)A+cos(n+1)Acos(n+2)A
= sinxsiny + cosxcosy
= cos(yx) = cosA