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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
A vertical po...
Question
A
vertical pole subtends an angle
tan
−
1
(
1
2
)
at a point
P
on the ground. The angle subtended by the upper half of the pole at
P
is
A
tan
−
1
(
1
4
)
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B
tan
−
1
(
1
8
)
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C
tan
−
1
(
2
3
)
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D
tan
−
1
(
2
9
)
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Solution
The correct option is
D
tan
−
1
(
2
9
)
as shown in the figure
t
a
n
(
t
a
n
−
1
(
1
2
)
)
=
1
2
=
2
h
b
.......................(1)
t
a
n
(
t
a
n
−
1
(
1
2
)
−
ϕ
)
=
h
b
.......................(2)
(1) divided by (2) we get
2
=
1
2
1
−
t
a
n
ϕ
2
1
+
t
a
n
ϕ
2
solving the above equation we get
t
a
n
ϕ
=
2
9
ϕ
=
t
a
n
−
1
2
9
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0
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