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Byju's Answer
Standard XII
Mathematics
Inverse Function
Number of sol...
Question
Number of solutions to the equation
tan
−
1
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
+
cos
−
1
(
x
)
=
3
π
4
−
sin
−
1
(
x
)
are
A
0
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B
1
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C
2
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D
3
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Solution
The correct option is
B
2
Given,
t
a
n
−
1
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
+
c
o
s
−
1
(
x
)
=
3
π
4
−
s
i
n
−
1
x
⟹
t
a
n
−
1
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
+
c
o
s
−
1
(
x
)
=
π
4
+
π
2
−
s
i
n
−
1
x
⟹
t
a
n
−
1
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
+
c
o
s
−
1
(
x
)
=
π
4
+
c
o
s
−
1
x
⟹
t
a
n
−
1
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
=
π
4
⟹
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
=
t
a
n
(
π
4
)
⟹
(
1
x
−
1
+
1
x
−
2
+
1
x
−
3
+
1
x
−
4
)
=
1
⟹
4
x
−
10
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
=
1
4
x
−
10
=
(
x
−
1
)
(
x
−
2
)
(
x
−
3
)
(
x
−
4
)
Hence the number of solution of
x
=
2
Suggest Corrections
0
Similar questions
Q.
Inverse circular functions,Principal values of
s
i
n
−
1
x
,
c
o
s
−
1
x
,
t
a
n
−
1
x
.
t
a
n
−
1
x
+
t
a
n
−
1
y
=
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
(a)
t
a
n
−
1
(
t
a
n
3
π
4
)
(b)
t
a
n
−
1
(
t
a
n
2
π
3
)
(c)
c
o
s
[
c
o
s
−
1
(
−
√
3
2
)
=
π
6
]
(d) If
a
≤
t
a
n
−
1
(
1
−
x
1
+
x
)
≤
b
where
0
≤
x
≤
1
Q.
Inverse circular functions,Principal values of
s
i
n
−
1
x
,
c
o
s
−
1
x
,
t
a
n
−
1
x
.
t
a
n
−
1
x
+
t
a
n
−
1
y
=
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
Evaluate
(a)
c
o
s
−
1
x
+
c
o
s
−
1
[
x
2
+
√
(
3
−
3
x
2
)
2
]
(
1
2
≤
x
≤
1
)
(b)
c
o
s
(
2
c
o
s
−
1
x
+
s
i
n
−
1
x
)
at
x
=
1
/
5
,
where
0
≤
c
o
s
−
1
x
≤
π
and
−
π
/
2
≤
s
i
n
−
1
x
≤
π
/
2
Q.
Inverse circular functions,Principal values of
s
i
n
−
1
x
,
c
o
s
−
1
x
,
t
a
n
−
1
x
.
t
a
n
−
1
x
+
t
a
n
−
1
y
=
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
(a)
s
i
n
−
1
(
1
−
x
)
−
2
s
i
n
−
1
x
=
π
/
2
.
(b) If
s
i
n
−
1
x
+
s
i
n
−
1
(
1
−
x
)
=
c
o
s
−
1
x
, then prove that x is equal to
0
,
1
/
2
.
Q.
Number of nonzero solutions
x
∈
[
−
π
,
3
π
]
of equation
cos
(
√
2
+
1
)
x
2
cos
(
√
2
−
1
)
x
2
=
1
is
Q.
Inverse circular functions,Principal values of
s
i
n
−
1
x
,
c
o
s
−
1
x
,
t
a
n
−
1
x
.
t
a
n
−
1
x
+
t
a
n
−
1
y
=
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
<
1
π
+
t
a
n
−
1
x
+
y
1
−
x
y
,
x
y
>
1
.
(a) If
t
a
n
−
1
(
x
+
2
x
)
−
t
a
n
−
1
4
x
−
t
a
n
−
1
(
x
−
2
x
)
=
0
then
x
=
.
.
.
.
.
.
.
.
.
.
or
x
=
.
.
.
.
.
.
.
.
(
x
ϵ
R
)
(b) If
s
i
n
−
1
x
+
s
i
n
−
1
y
=
2
π
/
3
c
o
s
−
1
x
−
c
o
s
−
1
y
=
π
/
3
then
x
=
.
.
.
.
.
.
.
.
,
y
=
.
.
.
.
.
.
.
(c) It
t
a
n
−
1
y
=
4
t
a
n
−
1
x
,
(
|
x
|
<
t
a
n
π
8
)
, then
express y as an algebraic function of x, Also deduce that
t
a
n
(
π
/
8
)
is a root of
x
4
−
6
x
2
+
1
=
0
.
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