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NIMCET 2020 Question Paper with solutions
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© examsnet.com
Question : 39
Total: 120
If
tan
x
2
=
tan
y
3
=
tan
z
5
and
x
+
y
+
z
=
π
,then the value of
tan
2
x
+
tan
2
y
+
tan
2
z
is
38/3
38
114
None of these
Validate
Solution:
x
+
y
+
z
=
π
Let
tan
x
2
=
tan
y
3
=
tan
z
5
=
1
∴
tan
x
+
tan
y
+
tan
z
=
tan
x
tan
y
tan
z
∴
2
λ
+
3
λ
+
5
λ
=
(
2
λ
)
(
3
λ
)
(
5
λ
)
10
λ
=
30
λ
3
λ
2
=
1
3
Now,
tan
2
x
+
tan
2
y
+
tan
2
z
4
λ
3
+
9
λ
2
+
25
λ
2
⇒
38
λ
2
=
38
×
1
3
=
38
3
© examsnet.com
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