If \( \mathrm{A}=45^{\circ} \), verify that : \[ \cos 2 \mathrm{~A}...

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If \( \mathrm{A}=45^{\circ} \), verify that :
\[
\cos 2 \mathrm{~A}=\cos ^{2} \mathrm{~A}-\sin ^{2} \mathrm{~A} .
\]
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