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India LIMIT
2020 LIMIT
2020 LIMIT Category 2
10
Trigonometry in a triangle
Trigonometry in a triangle
Source: LIMIT 2020 Cat 2 Obj P10
May 25, 2020
limit
trigonometry
geometry
Problem Statement
In a triangle
△
X
Y
Z
\triangle XYZ
△
X
Y
Z
,
tan
(
x
)
tan
(
z
)
=
2
\tan(x)\tan(z)=2
tan
(
x
)
tan
(
z
)
=
2
,
tan
(
y
)
tan
(
z
)
=
18
\tan(y)\tan(z)=18
tan
(
y
)
tan
(
z
)
=
18
. Then what is
tan
2
(
z
)
\tan^2(z)
tan
2
(
z
)
?
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