Rút gọn biểu thức \(M = \cos \left( {x + \frac{\pi }{4}} \right) + \sin \left( {x - \frac{\pi }{4}} \right)\)

* Hướng dẫn giải

\(\begin{array}{l}M = \cos \left( {x + \frac{\pi }{4}} \right) + \sin \left( {x - \frac{\pi }{4}} \right)\\ = \cos x\cos \frac{\pi }{4} - \sin x\sin \frac{\pi }{4} \\+ \sin x\cos \frac{\pi }{4} - \cos x\sin \frac{\pi }{4}\\ = \frac{{\sqrt 2 }}{2}\cos x - \frac{{\sqrt 2 }}{2}\sin x \\+ \frac{{\sqrt 2 }}{2}\sin x - \frac{{\sqrt 2 }}{2}\cos x = 0.\end{array}\)