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Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), whe...

Let `F_(k)(x)=1/k (sin^(k)x+cos^(k)x)`, where `x in R` and `k ge 1`, then find the value of `F_(4)(x)-F_(6)(x)`.

A

`5/12`

B

`-1/12`

C

`1/4`

D

`1/12`

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