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Byju's Answer
Standard XII
Mathematics
Logarithmic Inequalities
If tan x=34...
Question
If
tan
x
=
3
4
,
π
<
x
<
3
π
2
, then the value of
cos
x
2
is.
A
3
√
10
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B
−
3
√
10
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C
−
1
√
10
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D
1
√
10
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Solution
The correct option is
B
−
1
√
10
Given
tan
x
=
3
4
and
x
lies in third quadrant
cos
x
<
0
So
tan
2
x
=
9
16
⇒
sec
2
x
−
1
=
9
16
⇒
sec
2
x
=
25
16
⇒
cos
2
x
=
16
25
⇒
cos
x
=
−
4
5
Now using
cos
x
=
2
cos
2
x
2
−
1
cos
x
2
=
−
√
1
+
cos
x
2
=
−
⎷
1
−
4
5
2
=
−
1
√
10
Note: If
x
lies in the third quadrant, then
x
2
will lie in
2
n
d
quadrant
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0
Similar questions
Q.
If
tan
x
=
3
4
,
π
<
x
<
3
π
2
find value of
sin
x
2
,
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Q.
If
tan
x
=
3
4
,
π
<
x
<
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find the value of
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Q.
If
1
+
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log
10
√
2
+
x
+
4
log
10
√
2
−
x
=
3
log
10
√
4
−
x
2
, then the value of
x
is
Q.
If
1
+
3
log
10
√
2
+
x
+
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log
10
√
2
−
x
=
3
log
10
√
4
−
x
2
, then the value of
x
is
Q.
The set of real values of
t
∈
[
−
π
2
,
π
2
]
satisfying
2
sin
t
=
1
−
2
x
+
5
x
2
3
x
2
−
2
x
−
1
,
∀
x
∈
R
−
{
−
1
3
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}
lies in the interval
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