Question

Prove
= Cotx
cos(x - x)cos(-x)
sin(1 – x)cos
2​

Answer 1

To prove:- sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

Proof :−

L.H.S.=

sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x

=cos((n+2)x−(n−1)x){∵cos(A−B)=sinAsinB+cosAcosB}

⇒=cos((n+2−n−1)x)

⇒=cosx=R.H.S.

Hence proved..