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Mathematics
Mathematics
Problem
Let
t
1
=
(
sin
−
1
x
)
sin
−
1
x
t_1 = (\sin^{-1} x)^{\sin^{-1} x}
t
1
=
(
sin
−
1
x
)
s
i
n
−
1
x
,
t
2
=
(
sin
−
1
x
)
cos
−
1
x
t_2 = (\sin^{-1} x)^{\cos^{-1} x}
t
2
=
(
sin
−
1
x
)
c
o
s
−
1
x
,
t
3
=
(
cos
−
1
x
)
sin
−
1
x
t_3 = (\cos^{-1} x)^{\sin^{-1} x}
t
3
=
(
cos
−
1
x
)
s
i
n
−
1
x
,
t
4
=
(
cos
−
1
x
)
cos
−
1
x
t_4 = (\cos^{-1} x)^{\cos^{-1} x}
t
4
=
(
cos
−
1
x
)
c
o
s
−
1
x
, Match the following items of
Column I
with
Column II
Column I
Column II
A.
x
∈
(
0
,
cos
1
)
x \in (0, \cos 1)
x
∈
(
0
,
cos
1
)
(p)
t
1
>
t
2
>
t
4
>
t
3
t_1 > t_2 > t_4 > t_3
t
1
>
t
2
>
t
4
>
t
3
B.
x
∈
(
cos
1
,
1
2
)
x \in \left(\cos 1, \frac{1}{\sqrt{2}}\right)
x
∈
(
cos
1
,
2
1
)
(q)
t
4
>
t
3
>
t
1
>
t
2
t_4 > t_3 > t_1 > t_2
t
4
>
t
3
>
t
1
>
t
2
C.
x
∈
(
1
2
,
sin
1
)
x \in \left(\frac{1}{\sqrt{2}}, \sin 1\right)
x
∈
(
2
1
,
sin
1
)
(r)
t
2
>
t
1
>
t
4
>
t
3
t_2 > t_1 > t_4 > t_3
t
2
>
t
1
>
t
4
>
t
3
D.
x
∈
(
sin
1
,
1
)
x \in (\sin 1, 1)
x
∈
(
sin
1
,
1
)
(s)
t
3
>
t
4
>
t
1
>
t
2
t_3 > t_4 > t_1 > t_2
t
3
>
t
4
>
t
1
>
t
2
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