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AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper
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© examsnet.com
Question : 11
Total: 160
In triangle
A
B
C
,
tan
A
2
=
tan
b
3
=
tan
c
4
then the value of
sec
2
A
+
sec
2
B
+
sec
2
C
=
101
8
111
8
121
8
91
8
Validate
Solution:
In a
△
A
B
C
, it is given that
tan
A
2
=
tan
B
3
=
tan
C
4
=
k
(Let)
⇒
tan
A
=
2
k
,
tan
B
=
3
k
and
tan
c
=
4
k
.
Since in
△
A
B
C
,
tan
A
+
tan
B
+
tan
C
=
tan
A
tan
B
tan
C
⇒
9
k
=
24
k
3
⇒
k
2
=
3
8
{
∵
k
≠
0
}
Now,
sec
2
A
+
sec
2
B
+
sec
2
C
=
3
+
tan
2
A
+
tan
2
B
+
tan
2
C
=
3
+
k
2
[
4
+
9
+
16
]
=
3
+
3
8
(
29
)
=
24
+
87
8
=
111
8
© examsnet.com
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