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Trả lời:
$\begin{array}{l}VT=\dfrac{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}-\cos\bigg{(}\dfrac{\pi}{4}+x\bigg{)}}{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}+\cos\bigg{(}\dfrac{\pi}{4}+x\bigg{)}}=\dfrac{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}-\sin\bigg{(}\dfrac{\pi}{4}-x\bigg{)}}{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}+\sin\bigg{(}\dfrac{\pi}{4}-x\bigg{)}}\\=\dfrac{2.\cos\dfrac{\pi}{4}.\sin x}{2.\sin\dfrac{\pi}{4}.\cos x}=\dfrac{\dfrac{\sqrt{2}}{2}.\sin x}{\dfrac{\sqrt{2}}{2}.\cos x}=\dfrac{\sin x}{\cos x}=\tan x=VP\end{array}$
Vậy $\dfrac{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}-\cos\bigg{(}\dfrac{\pi}{4}+x\bigg{)}}{\sin\bigg{(}\dfrac{\pi}{4}+x\bigg{)}+\cos\bigg{(}\dfrac{\pi}{4}+x\bigg{)}}=\tan x$ (ĐPCM).
