Đáp án:
$\begin{array}{l}
A = \dfrac{{\sin \left( {\dfrac{\pi }{4} - x} \right) + \cos \left( {\dfrac{\pi }{4} - x} \right)}}{{\sin \left( {\dfrac{\pi }{4} - x} \right) - \cos \left( {\dfrac{\pi }{4} - x} \right)}}\\
= \dfrac{{\sin \dfrac{\pi }{4}.sinx - \cos \dfrac{\pi }{4}.\cos x + \cos \dfrac{\pi }{4}.sinx + sin\dfrac{\pi }{4}.cosx}}{{\sin \dfrac{\pi }{4}.sinx - \cos \dfrac{\pi }{4}.\cos x - \cos \dfrac{\pi }{4}.sinx - sin\dfrac{\pi }{4}.cosx}}\\
= \dfrac{{\sin x - \cos x + \sin x + \cos x}}{{\sin x - \cos x - \sin x - \cos x}}\\
\left( {do:\sin \dfrac{\pi }{4} = \cos \dfrac{\pi }{4} = \dfrac{{\sqrt 2 }}{2}} \right)\\
= \dfrac{{2\sin x}}{{ - 2\cos x}}\\
= - \tan x
\end{array}$
