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Mathematics
Mathematics
Problem
For
0
<
x
<
π
2
0 < x < \frac{\pi}{2}
0
<
x
<
2
π
, let
P
m
n
(
x
)
=
m
log
cos
x
(
sin
x
)
+
n
log
cos
x
(
cot
x
)
P_{mn}(x) = m \log_{\cos x}(\sin x) + n \log_{\cos x}(\cot x)
P
mn
(
x
)
=
m
lo
g
c
o
s
x
(
sin
x
)
+
n
lo
g
c
o
s
x
(
cot
x
)
, where
m
,
n
∈
{
1
,
2
,
…
,
9
}
m, n \in \{1, 2, \dots, 9\}
m
,
n
∈
{
1
,
2
,
…
,
9
}
. If
P
34
(
x
)
=
P
22
(
x
)
P_{34}(x) = P_{22}(x)
P
34
(
x
)
=
P
22
(
x
)
, then
sin
x
\sin x
sin
x
is expressed as
(
q
−
1
p
)
\left(\frac{\sqrt{q} - 1}{p}\right)
(
p
q
−
1
)
. Find
(
p
+
q
)
(p + q)
(
p
+
q
)
. a. 3 b. 4 c. 7 d. 9
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