若sin⁴x＜cos⁴x，则x的取值范围是（  ）

A：$\left\{x\text{|}2k\pi \text{-}\frac{3\pi }{4}＜x＜2k\pi +\frac{\pi }{4}\text{,}k\in z\right\}$

B：$\left\{x\text{|}2k\pi +\frac{\pi }{4}＜x＜2k\pi +\frac{5\pi }{4}\text{,}k\in z\right\}$

C：$\left\{x\text{|}k\pi \text{-}\frac{\pi }{4}＜x＜k\pi +\frac{\pi }{4}\text{,}k\in z\right\}$

D：$\left\{x\text{|}k\pi +\frac{\pi }{4}＜x＜k\pi +\frac{3\pi }{4}\text{,}k\in z\right\}$