If $x + y = \dfrac{\pi}{4}$, then $(1 + \tan x)(1 + \tan y) =$

The value of $\cos 15^\circ - \sin 15^\circ$ is ......

The value of $\cos\left(\dfrac{\pi}{5}\right)$ is ...

Let $f_k(x) = \dfrac{1}{k}(\cos^k x + \sin^k x)$ where $k \in N$, then $f_6(x) - f_4(x) = \ldots$