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UPSC NDA I 2010 Mathematics Paper
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© examsnet.com
Question : 3
Total: 120
The angle A lies in the third quadrant and it satisfies the equation
4
(
sin
2
x
+
cos
x
)
=
1
. What is the measure of the angle
A
?
225
∘
240
∘
210
∘
None of these
Validate
Solution:
4
(
sin
2
x
+
cos
x
)
=
1
4
(
1
−
cos
2
x
+
cos
x
)
=
1
−
cos
2
x
+
cos
x
=
1
4
−
1
=
−
3
4
cos
2
x
−
cos
x
−
3
4
=
0
Multiply both sides by 4
4
cos
2
x
−
4
cos
x
−
3
=
0
Let,
a
=
cos
x
4
a
2
−
4
a
−
3
=
0
4
a
2
−
6
a
+
2
a
−
3
=
0
2
a
(
2
a
−
3
)
+
1
(
2
a
−
3
)
=
0
a
=
−
1
2
,
a
=
−
3
2
are not valid
Now,
cos
x
=
cos
(
π
−
π
∕
3
)
cos
x
=
cos
2
π
∕
3
x
=
2
π
∕
3
=
2
×
180
3
=
120
∘
© examsnet.com
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