JEE Math Practice 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. A.$${1 \over 4}$$
2. B.$${1 \over 12}$$
3. C.$${1 \over 6}$$
4. D.$${1 \over 3}$$