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

If $\tan A$ and $\tan B$ are the roots of the equation $5x^2 - 4x + 1 = 0$, then the value of $A + B$ is...

If $\cos 43^\circ + \sin 43^\circ = k^3$, then $\cos 2^\circ = \ldots$

The value of $\cos(60^\circ - A)\cdot\cos A\cdot\cos(60^\circ + A)$ is