Question

cos alpha does not equal to 0,cos alpha by 2 does not equal to 0 then sin((n+1)alpha)-sin((n-1)alpha)/cos((n+1)alpha)+cos((n-1)alpha)+2cosn alpha​

Answer 1

Step-by-step explanation:

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)