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Mathematics
Mathematics
Problem
If
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
,
k
≥
1
x \in \mathbb{R}, k \ge 1
x
∈
R
,
k
≥
1
, then
f
4
(
x
)
−
f
6
(
x
)
f_4(x) - f_6(x)
f
4
(
x
)
−
f
6
(
x
)
is equal to a.
1
6
\frac{1}{6}
6
1
b.
1
3
\frac{1}{3}
3
1
c.
1
4
\frac{1}{4}
4
1
d.
1
12
\frac{1}{12}
12
1
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