Trigonometry
posted by Kewal .
Prove that
sin(n+1)Asin(n1)A + cos(n+1)Acos(n1)A = cos2A

Let (n+1)A = x
Let (n1)A = y
sinx*siny + cosx*cosy = cos (x  y)
(This is an identity you should know)
Now note that x y = 2A , so
sinx*siny + cosx*cosy = cos (x  y)
= cos(2A)