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Mathematics
Mathematics
Problem
- Let
θ
∈
(
0
,
π
4
)
\theta \in \left(0, \frac{\pi}{4}\right)
θ
∈
(
0
,
4
π
)
and
t
1
=
(
tan
θ
)
tan
θ
t_1 = (\tan \theta)^{\tan \theta}
t
1
=
(
tan
θ
)
t
a
n
θ
,
t
2
=
(
tan
θ
)
cot
θ
t_2 = (\tan \theta)^{\cot \theta}
t
2
=
(
tan
θ
)
c
o
t
θ
,
t
3
=
(
cot
θ
)
tan
θ
t_3 = (\cot \theta)^{\tan \theta}
t
3
=
(
cot
θ
)
t
a
n
θ
and
t
4
=
(
cot
θ
)
cot
θ
t_4 = (\cot \theta)^{\cot \theta}
t
4
=
(
cot
θ
)
c
o
t
θ
, then show that
t
4
>
t
3
>
t
1
>
t
2
t_4 > t_3 > t_1 > t_2
t
4
>
t
3
>
t
1
>
t
2
.
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