Let Fkx-1ksin kx-coskx- where x- and k- 1- then find the value of F4x-F0x-

F _ k (x)= 1 k (sin ^ k x +cos ^ k x ) F _ 4 (x) F _ 0 (x) =k≥ 1 ∴∞ which is not possible. ∴ F _ 4 (x)=sin ^ 4 x +cos ^ 4 x #160; ...

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Definition of Functions

Let Fkx=1ks...

Question

Let $F_{k} (x) = \frac{1}{k} ({sin}^{k} x + {cos}^{k} x)$ , where $x \in R$ and $k \geq 1$ , then find the value of $F_{4} (x) - F_{0} (x)$ .

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