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KEAM 2013 Math Paper
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© examsnet.com
Question : 47
Total: 120
If
0
<
x
<
π
2
,
then
tan
(
π
4
+
x
2
)
+
tan
(
π
4
−
x
2
)
is equal to
2
s
e
c
x
2
c
o
s
x
s
e
c
x
c
o
s
x
2
s
i
n
x
Validate
Solution:
Given,
0
<
x
<
π
2
, then
tan
(
π
4
+
x
2
)
+
tan
(
π
4
−
x
2
)
=
1
+
tan
x
2
1
−
tan
x
2
+
1
−
tan
x
2
1
+
tan
x
2
=
(
1
+
tan
x
2
)
2
+
(
1
−
tan
x
2
)
2
(
1
−
tan
2
x
2
)
=
2
(
1
+
tan
2
x
2
)
(
1
−
tan
2
x
2
)
=
2
(
sin
2
x
/
2
+
cos
2
x
/
2
)
(
cos
2
x
/
2
−
sin
2
x
/
2
)
=
2
⋅
1
cos
x
=
2
sec
x
© examsnet.com
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