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UPSC NDA 2 2021 Mathematics Solved Paper
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© examsnet.com
Question : 29
Total: 120
Let
sin
x
+
sin
y
=
cos
x
+
cos
y
for all
x
,
y
∈
ℝ
. What is
tan
(
x
2
+
y
2
)
equal to?
[NDA-II 2021]
1
2
√
2
2
√
2
Validate
Solution:
👈: Video Solution
(a) Given that,
sin
x
+
sin
y
=
cos
x
+
cos
y
∀
x
∈
C
2
sin
(
x
+
y
2
)
cos
(
x
−
y
2
)
=
2
cos
(
x
+
y
2
)
⋅
cos
(
x
−
y
2
)
⇒
2
sin
(
x
+
y
2
)
⋅
cos
(
x
−
y
2
)
2
cos
(
x
+
y
2
)
⋅
cos
(
x
−
y
2
)
=
1
tan
(
x
+
y
2
)
=
1
or
tan
(
x
2
+
y
2
)
=
1
Hence, option (a) is correct.
© examsnet.com
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