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Trả lời:
$\cos^2\bigg{(}\dfrac{\pi}{4}+\alpha\bigg{)}-\cos^2\bigg{(}\dfrac{\pi}{4}-\alpha\bigg{)}$
$=\cos^2\bigg{(}\dfrac{\pi}{4}+\alpha\bigg{)}-\sin^2\bigg{[}\dfrac{\pi}{2}-\bigg{(}\dfrac{\pi}{4}-\alpha\bigg{)}\bigg{]}$
$=\cos^2\bigg{(}\dfrac{\pi}{4}+\alpha\bigg{)}-\sin^2\bigg{(}\dfrac{\pi}{4}+\alpha\bigg{)}$
$=\cos\bigg{(}\dfrac{\pi}{2}+2\alpha\bigg{)}$
$=\cos\bigg{[}\dfrac{\pi}{2}-\bigg{(}-2\alpha\bigg{)}\bigg{]}$
$=\sin(-2\alpha)$
$=-\sin 2\alpha$.
