Let $$fk\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,.$$
Then $${f_4}\left( x \right) - {f_6}\left( x \right)\,\,$$ equals
A
$${1 \over 4}$$
B
$${1 \over 12}$$
C
$${1 \over 6}$$
D
$${1 \over 3}$$
Explanation
Let $${f_k}\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}.x} \right)$$
Consider
$${f_4}\left( x \right) - {f_6}\left( x \right) $$
$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \bot CD.$$ If $$\angle ADB = \theta ,\,BC = p$$ and $$CD = q,$$ then AB is equal to: