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Mathematics
Mathematics
Problem
Maximum value of the differentiable function which satisfies the equation
f
(
x
)
=
−
∫
0
x
f
(
t
)
tan
t
d
t
+
∫
0
x
tan
(
t
−
x
)
d
t
f(x) = -\int_{0}^{x} f(t) \tan t\, dt + \int_{0}^{x} \tan(t-x)\, dt
f
(
x
)
=
−
∫
0
x
f
(
t
)
tan
t
d
t
+
∫
0
x
tan
(
t
−
x
)
d
t
, where
x
∈
(
−
π
2
,
π
2
)
x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)
x
∈
(
−
2
π
,
2
π
)
is
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