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Byju's Answer
Standard XII
Mathematics
Complex Numbers
If x ∈ 0, 1...
Question
If
x
∈
(
0
,
1
)
then value of
tan
−
1
(
1
−
x
2
2
x
)
+
cos
−
1
(
1
−
x
2
1
+
x
2
)
is?
A
π
2
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B
−
π
2
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C
0
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D
π
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Solution
The correct option is
A
π
2
tan
−
1
(
1
−
x
2
2
x
)
+
cos
−
1
(
1
−
x
2
1
+
x
2
)
Put
x
=
tan
θ
=
tan
−
1
(
cot
2
θ
)
+
cos
−
1
cos
2
θ
=
tan
−
1
(
tan
(
π
2
−
2
θ
)
)
+
2
θ
=
π
2
−
2
θ
+
2
θ
=
π
2
Suggest Corrections
0
Similar questions
Q.
(a) Prove that
sin
[
t
a
n
−
1
1
−
x
2
2
x
+
cos
−
1
1
−
x
2
1
+
x
2
]
=
1
.
(b) If
sin
−
1
(
x
−
x
2
2
+
x
3
4
−
.
.
.
.
.
)
+
cos
−
1
(
x
2
−
x
4
2
+
x
6
4
−
.
.
.
.
.
.
.
)
=
π
2
for
0
<
|
x
|
<
√
2
, then x equals
Q.
If
cot
−
1
(
1
x
)
+
cos
−
1
(
−
x
)
+
tan
−
1
x
=
π
and
sin
−
1
x
<
0
,
then the value of
(
1
−
x
2
)
3
/
2
x
2
is
Q.
If
cos
−
1
(
1
−
x
2
1
+
x
2
)
+
cos
−
1
(
1
−
y
2
1
+
y
2
)
=
π
2
, where
x
y
<
1
, then
Q.
If
t
a
n
−
1
2
x
1
−
x
2
+
c
o
t
−
1
1
−
x
2
2
x
=
π
/
3
,
x
>
0
then
25
(
x
4
+
1
x
4
)
+
8
is equal to
Q.
if
x
ϵ
(
0
,
1
)
, then the value of
t
a
n
−
1
(
1
−
x
2
2
x
)
+
c
o
s
−
1
(
1
−
x
2
1
+
x
2
)
is equal to
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