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UPSC NDA II 2011 Mathematics Paper
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© examsnet.com
Question : 2
Total: 120
What is the value of
tan
9
∘
−
tan
27
∘
−
tan
63
∘
+
tan
81
∘
?
1
2
3
4
Validate
Solution:
We have,
tan
9
∘
−
tan
27
∘
−
tan
63
∘
+
tan
81
∘
=
(
tan
9
∘
+
tan
81
∘
)
−
(
tan
27
∘
+
tan
63
∘
)
=
1
cos
9
∘
⋅
cos
81
∘
−
1
cos
27
∘
⋅
cos
63
∘
=
1
sin
9
∘
⋅
cos
9
∘
−
1
sin
27
∘
⋅
cos
27
∘
=
2
sin
18
∘
−
2
sin
54
∘
=
2
[
sin
54
∘
−
sin
18
∘
sin
54
∘
⋅
sin
18
∘
]
=
2
[
2
cos
36
∘
⋅
sin
18
∘
sin
18
∘
⋅
cos
36
∘
]
=
2
×
2
=
4
.
© examsnet.com
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