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If $\cos (A+B)=\alpha \cos A \cos B+\beta \sin A \sin B$, then $(\alpha, \beta)=$
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Verified Answer
The correct answer is:
$(1,-1)$
Given $\cos (A+B)=\alpha \cos A \cos B+\beta \sin A \sin B$
$\begin{aligned}
& \text { But } \cos (A+B)=\cos A \cos B-\sin A \sin B \\
& \Rightarrow \alpha=1, \beta=-1 .
\end{aligned}$
$\begin{aligned}
& \text { But } \cos (A+B)=\cos A \cos B-\sin A \sin B \\
& \Rightarrow \alpha=1, \beta=-1 .
\end{aligned}$
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