Question

sin (n + 1)x sin (n + 2)x+cos (n + 1)x cos (n + 2)r = cos x ​

Answer 1

${\huge{\underline{\large{\mathbb{ \green{VERIFIED \: ANSWER}}}}}}$

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.