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Question
Mathematics
If tan x = (3/4), π < x < (3π/2) then the value of cos (x/2) is
Q. If tan
x
=
4
3
,
π
<
x
<
2
3
π
then the value of
cos
2
x
is
3348
192
KCET
KCET 2014
Trigonometric Functions
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A
10
3
27%
B
−
10
3
29%
C
−
10
1
31%
D
10
1
14%
Solution:
Given,
tan
x
=
4
3
,
π
<
x
<
2
3
π
⇒
cos
x
=
−
5
4
∵
1
+
cos
x
=
2
cos
2
(
2
x
)
∴
1
−
5
4
=
2
cos
2
(
2
x
)
⇒
5
1
=
2
cos
2
(
2
x
)
⇒
cos
2
(
2
x
)
=
10
1
⇒
cos
(
2
x
)
=
±
10
1
cos
(
2
x
)
=
−
10
1
[
∵
2
π
<
2
x
<
4
3
π
]