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

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

Yuvraj Singh 6 years, 1 month ago

Taking LHS Let (n+1) = A and (n+2)=B Sin (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

Lucky Papa 6 years, 1 month ago

We know that, CosACosB+SinASinB=Cos (A-B) Using this Identity So, =Cos (n+2-n-1)x =Cosx=RHS Hence Proved.
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