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Mathematics
Mathematics
Problem
If
P
=
(
tan
(
3
n
+
1
θ
)
−
tan
θ
)
P = (\tan(3^{n+1}\theta) - \tan \theta)
P
=
(
tan
(
3
n
+
1
θ
)
−
tan
θ
)
and
Q
=
∑
r
=
0
n
sin
(
3
r
θ
)
cos
(
3
r
+
1
θ
)
Q = \sum_{r=0}^{n} \frac{\sin(3^r \theta)}{\cos(3^{r+1}\theta)}
Q
=
∑
r
=
0
n
c
o
s
(
3
r
+
1
θ
)
s
i
n
(
3
r
θ
)
, then such that
π
<
α
−
β
<
3
π
\pi < \alpha - \beta < 3\pi
π
<
α
−
β
<
3
π
(a)
P
=
2
Q
P = 2Q
P
=
2
Q
(b)
P
=
3
Q
P = 3Q
P
=
3
Q
(c)
2
P
=
Q
2P = Q
2
P
=
Q
(d)
3
P
=
Q
3P = Q
3
P
=
Q
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