Question

Prove sin(n+1)sin(n+2)x+cos(n+1)x cos(n+2)x = sin(x+y).

Answer 1

Following are the prove of given question is given below

Explanation:

In the given question RHS side is incorrect .The correct question is

sin(n+1)x sin(n+2)x + cos(n+1)x cos(n+2)x = cosx

LHS

`sin(n+1)x\ sin(n+2)x+cos(n+1)x\ cos(n+2)x\\We\ know\ that\\cos(x-y)\ = cos\ x\ cos\ y\ +\ sin\ x\ sin\ y`

Here

x =(n+1)x

y=(n+2)x

So

`cos((n+1)x-(n+2)x)\\\cos(nx + x- nx-2x)`

cos(-x)

cos(x) =RHS