Let $f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$ where $x \in R$ and $k \ge \,1.$ Then ${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$ equals :

Question

Let $f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$ where $x \in R$ and $k \ge \,1.$
Then ${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$ equals :

${1 \over 4}$