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Byju's Answer
Standard XII
Mathematics
Basic Inverse Trigonometric Functions
All x satisfy...
Question
All
x
satisfying the inequality
(
cot
−
1
x
)
2
−
7
(
cot
−
1
x
)
+
10
>
0
, lie in the interval :
A
(
cot
5
,
cot
4
)
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B
(
cot
2
,
∞
)
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C
(
−
∞
,
cot
5
)
∪
(
cot
4
,
cot
2
)
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D
(
−
∞
,
cot
5
)
∪
(
cot
2
,
∞
)
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Solution
The correct option is
B
(
cot
2
,
∞
)
(
cot
−
1
x
)
2
−
7
(
cot
−
1
x
)
+
10
>
0
⇒
(
cot
−
1
x
−
2
)
(
cot
−
1
x
−
5
)
>
0
⇒
cot
−
1
x
∈
(
−
∞
,
2
)
∪
(
5
,
∞
)
⋯
(
1
)
We know that
cot
−
1
x
∈
(
0
,
π
)
⋯
(
2
)
So, from
(
1
)
and
(
2
)
0
<
cot
−
1
x
<
2
As,
cot
−
1
x
is decreasing function,
⇒
x
∈
(
cot
2
,
∞
)
Suggest Corrections
1
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