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UPSC NDA Math Model Paper 9
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© examsnet.com
Question : 58
Total: 120
If α and β are positive angles such that α + β =
π
4
, then what is (1 + tan α) (1 + tan β) equal to?
0
1
2
3
Validate
Solution:
Given,
α
and
β
are positive angles such that
α
+
β
=
π
4
,
⇒
tan
(
α
+
β
)
=
tan
(
π
4
)
⇒
tan
α
+
tan
β
1
−
tan
α
tan
β
=
1
⇒
tan
α
+
tan
β
=
1
−
tan
α
tan
β
⇒
tan
α
+
tan
α
tan
β
+
tan
β
−
1
=
0
⇒
tan
α
+
tan
α
tan
β
+
tan
β
+
1
−
2
=
0
⇒
tan
α
+
tan
α
tan
β
+
tan
β
+
1
=
2
⇒
tan
α
(
1
+
tan
β
)
+
(
1
+
tan
β
)
=
2
⇒
(
1
+
tan
α
)
(
1
+
tan
β
)
=
2
Hence, If α and β are positive angles such that
α
+
β
=
π
4
, then (1 + tan α) (1 + tan β) equal to 2.
© examsnet.com
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