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JEE Main Math Class 12 Inverse Trigonometric Functions Questions
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© examsnet.com
Question : 37
Total: 74
The value of
tan
(
2
tan
−
1
(
3
5
)
+
sin
−
1
(
5
13
)
)
is equal to
[2021, 20 July Shift-II]
−
181
69
220
21
−
291
76
151
63
Validate
Solution:
Let
A
=
tan
(
2
tan
−
1
(
3
5
)
+
sin
−
1
(
5
13
)
)
. . . (i)
Now, using
2
tan
−
1
x
=
tan
−
1
2
x
1
−
x
2
2
tan
−
1
(
3
5
)
=
tan
−
1
(
2
(
3
5
)
1
−
(
3
5
)
2
)
=
tan
−
1
(
6
5
1
−
9
25
)
=
tan
−
1
(
30
16
)
=
tan
−
1
(
15
8
)
Let
sin
−
1
(
5
13
)
=
θ
, then
sin
θ
=
5
13
∴
tan
θ
=
sin
θ
√
1
−
sin
2
θ
=
5
13
√
1
−
(
5
3
)
2
=
5
13
12
13
⇒
θ
=
tan
−
1
(
5
12
)
=
sin
−
1
(
5
13
)
From Eq. (i),
A
=
tan
(
tan
−
1
(
15
8
)
+
tan
−
1
(
5
12
)
)
=
tan
[
tan
−
1
(
15
8
+
5
12
1
−
(
15
8
)
(
5
12
)
]
]
=
tan
[
tan
−
1
(
55
24
21
96
)
]
=
tan
[
tan
−
1
55
×
4
21
]
=
tan
(
tan
−
1
220
21
)
=
220
21
© examsnet.com
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