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UPSC NDA Math Model Paper 9
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© examsnet.com
Question : 10
Total: 120
Given that cot α and cot β are the roots of the equation
2
x
2
+
3
x
+
4
=
0
. What is the cot (α + β) equal to
−
3
2
4
3
−
2
3
3
4
Validate
Solution:
Here,
cot
α
and
cot
β
are the roots of the equation
2
x
2
+
3
x
+
4
=
0
Sum of roots
=
cot
α
+
cot
β
=
−
3
∕
2
Product of roots
=
cot
α
×
cot
β
=
4
∕
2
=
2
tan
(
α
+
β
)
=
tan
α
+
tan
β
1
−
tan
α
tan
β
=
1
cot
α
+
1
cot
β
1
−
1
cot
α
×
1
cot
β
=
cot
α
+
cot
β
cot
α
cot
β
−
1
=
−
3
2
2
−
1
=
−
3
2
cot (α + β) = -2/3
Hence, option (3) is correct.
© examsnet.com
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