Chứng minh rằng: a) sin x – cos x = \(\sqrt 2 \sin \left( {x - \frac{\pi }{4}} \right)\); b) \(\tan \left( {\frac{\pi }{4} - x} \right) = \frac\,\,\,\)\(\left( {x \ne \frac{\pi }{2} + k\pi ,\,\,x \ne \frac{{3\pi }}{4} + k\pi ,k \in \mathbb{Z}} \right)\).