\(y=\cos(2x+ \dfrac{\pi}{4}) +\sin(2x-\dfrac{\pi}{4})\)
\(=\dfrac{\sqrt 2}{2}\cos 2x-\dfrac{\sqrt 2}{2}\sin 2x+\dfrac{\sqrt 2}{2}\sin 2x-\dfrac{\sqrt 2}{2}\cos 2x\)
\(=0\)
TXĐ: \(D=\mathbb R\)
Khi đó \(x\in D\) \(\Rightarrow \exists (-x)\in D\)
Xét: \(y(-x)=\cos(-2x+ \dfrac{\pi}{4}) +\sin(-2x-\dfrac{\pi}{4})\)
\(=\dfrac{\sqrt 2}{2}\cos (-2x)-\dfrac{\sqrt 2}{2}\sin (-2x)+\dfrac{\sqrt 2}{2}\sin (-2x)-\dfrac{\sqrt 2}{2}\cos (-2x)=0=y(x)\)
Vậy hàm đã cho là hàm chẵn.
