Respuesta :
Answer:
Following are the prove of given question is given below
Step-by-step 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
[tex]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[/tex]
Here
x =(n+1)x
y=(n+2)x
So
[tex]cos((n+1)x-(n+2)x)\\\cos(nx + x- nx-2x)[/tex]
cos(-x)
cos(x) =RHS
