\(\mathop {\lim }\limits_{x \to \frac{\pi }{4}} \frac{{{\mathop{\rm s}\nolimits} {\rm{inx}} - c{\rm{osx}}}}{{\tan \left( {\frac{\pi }{4} - x} \right)}

* Hướng dẫn giải

\(\mathop {\lim }\limits_{x \to \frac{\pi }{4}} \frac{{{\mathop{\rm s}\nolimits} {\rm{inx}} - c{\rm{osx}}}}{{\tan \left( {\frac{\pi }{4} - x} \right)}} = \mathop {\lim }\limits_{x \to \frac{\pi }{4}} \frac{{\sqrt 2 \sin \left( {x - \frac{\pi }{4}} \right)}}{{\tan \left( {\frac{\pi }{4} - x} \right)}} = \mathop {\lim }\limits_{x \to \frac{\pi }{4}} \left[ { - \sqrt 2 \cos \left( {x - \frac{\pi }{4}} \right)} \right] =  - \sqrt 2 \)