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Mathematics
Mathematics
Problem
Let
F
k
(
x
)
=
1
k
(
sin
k
x
+
cos
k
x
)
F_k(x) = \frac{1}{k}(\sin^k x + \cos^k x)
F
k
(
x
)
=
k
1
(
sin
k
x
+
cos
k
x
)
, where
x
∈
R
x \in \mathbb{R}
x
∈
R
and
k
≥
1
k \ge 1
k
≥
1
, then find the value of
F
4
(
x
)
−
F
6
(
x
)
F_4(x) - F_6(x)
F
4
(
x
)
−
F
6
(
x
)
.
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