Sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx

1.	Sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx
Answer» Taking LHS Let (n+1) = Aand (n+2)=BSin (n+1)xsin (n+2)x +cos (n+1)xcos (n+2)x=sinAxsinBx +cosAxcosBx=cos [(n+1)x - (n+2)x]=cos x (n+1-n-2)=cos(-x)=cosx<br>We know that,CosACosB+SinASinB=Cos (A-B)Using this IdentitySo,=Cos (n+2-n-1)x=Cosx=RHS Hence Proved.

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