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Mathematics
Mathematics
Problem
If the area enclosed by the curves
f
(
x
)
=
cos
−
1
(
cos
x
)
and
g
(
x
)
=
sin
−
1
(
cos
x
)
in
x
∈
[
9
π
4
,
15
π
4
]
f(x) = \cos^{-1}(\cos x) \text{ and } g(x) = \sin^{-1}(\cos x) \text{ in } x \in \left[ \frac{9\pi}{4}, \frac{15\pi}{4} \right]
f
(
x
)
=
cos
−
1
(
cos
x
)
and
g
(
x
)
=
sin
−
1
(
cos
x
)
in
x
∈
[
4
9
π
,
4
15
π
]
is
a
π
2
b
\frac{a\pi^2}{b}
b
a
π
2
(where
a
a
a
and
b
b
b
are coprime), then find
(
a
−
b
)
(a-b)
(
a
−
b
)
.
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