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Let $f_k(x) = \frac{1}{k}(\sin^k x + \cos^k x)$ for $k = 1, 2, 3, \ldots$ Then for all $x \in \mathbb{R}$, the value of $f_4(x) - f_6(x)$ is equal to:
(1) $\frac{1}{12}$
(2) $\frac{1}{4}$
(3) $\frac{-1}{12}$
(4) $\frac{5}{12}$
Type: MCQ
$f_4(x) - f_6(x) = \frac{1}{4} - \frac{1}{6} = \frac{1}{12}$
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