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Tardigrade
Question
Mathematics
tan[(1/2) sin-1 ((2x/1+x2)) + (1/2) cos-1 ((1-x2/1+x2))] =
Q.
tan
[
2
1
sin
−
1
(
1
+
x
2
2
x
)
+
2
1
cos
−
1
(
1
+
x
2
1
−
x
2
)
]
=
4860
248
COMEDK
COMEDK 2007
Inverse Trigonometric Functions
Report Error
A
∞
15%
B
1
26%
C
1
−
x
2
2
x
30%
D
1
+
x
2
2
x
28%
Solution:
tan
[
2
1
sin
−
1
(
1
+
x
2
2
x
)
+
2
1
cos
−
1
(
1
+
x
2
1
−
x
2
)
]
Putting
x
=
tan
θ
⇒
θ
=
tan
−
1
x
=
tan
[
2
1
sin
−
1
(
1
+
t
a
n
2
θ
2
t
a
n
θ
)
+
2
1
cos
−
1
(
1
+
t
a
n
2
θ
1
−
t
a
n
2
θ
)
]
=
tan
(
2
1
sin
−
1
(
sin
2
θ
)
+
2
1
cos
−
1
(
cos
2
θ
)
)
=
tan
(
2
2
θ
+
2
2
θ
)
=
tan
(
2
θ
)
=
tan
(
2
tan
−
1
x
)
=
tan
(
tan
−
1
(
1
−
x
2
2
x
)
)
=
1
−
x
2
2
x