Question
Prove that:
$
\begin{array}{l}
\sin (n+1) A \sin (n+2) A+\cos (n+1) A \cos (n+2) A=\cos A
\end{array}
$
$
\begin{array}{l}
\sin (n+1) A \sin (n+2) A+\cos (n+1) A \cos (n+2) A=\cos A
\end{array}
$
✓
Answer
$\begin{array}{l}\text { L.H.S. }=\sin (n+1) A \sin (n+2) A+\cos (n+1) \\A \cos (n+2) A \\\Rightarrow \quad \cos (n+2) A \cos (n+1) A+\sin (n+2) A \sin (n+1) A \\\Rightarrow \quad \cos [(n+2) A-(n+1) A]= \cos [(n+2-n-1) A] \\=\cos A=RHS\end{array}$
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