Let $\;f_{k}(x)= \large\frac{1}{k}(sin^{k}x+cos^{k}x)\;$ where $\;x \in R\;$ and $\;k \geq 1\;$. Then $\;f_{4}(x) - f_{6}(x)$ equals :

Question

$(a)\;\large\frac{1}{4} \qquad(b)\;\large\frac{1}{12}\qquad(c)\;\large\frac{1}{6}\qquad(d)\;\large\frac{1}{3}$