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Byju's Answer
Standard XII
Mathematics
Parametric Differentiation
Inverse circu...
Question
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
.
4
t
a
n
−
1
1
5
−
t
a
n
−
1
1
70
+
t
a
n
−
1
1
99
=
π
4
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Solution
2
t
a
n
−
1
1
5
=
t
a
n
−
1
2
/
5
1
−
(
1
/
25
)
=
t
a
n
−
1
5
12
.
∴
4
t
a
n
−
1
1
5
=
2
t
a
n
−
1
5
12
t
a
n
−
1
2
(
5
/
12
)
1
−
(
25
/
144
)
=
t
a
n
−
1
120
119
.
∴
L
.
H
.
S
.
=
t
a
n
−
1
120
119
−
(
t
a
n
−
1
1
70
−
t
a
n
−
1
1
99
)
=
t
a
n
−
1
120
119
−
t
a
n
−
1
1
/
70
−
1
/
99
1
+
(
1
+
99
)
(
1
/
70
)
=
t
a
n
−
1
120
119
−
t
a
n
−
1
29
6931
=
t
a
n
−
1
120
119
−
t
a
n
−
1
1
239
=
t
a
n
−
1
120
/
119
−
1
/
239
1
+
(
120
/
119
)
.
(
1
/
239
)
=
t
a
n
−
1
120.239
−
119
119.239
+
120
=
t
a
n
−
1
119.239
+
(
239
+
119
)
119.239
+
120
=
t
a
n
−
1
1
=
π
/
4
writing
120
x
=
(
119
+
1
)
x
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)
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.
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) Given
0
≤
x
≤
1
2
then the value of
t
a
n
[
s
i
n
−
1
{
x
√
2
+
√
1
−
x
2
√
2
}
−
s
i
n
−
1
x
]
is
(b) If
α
=
s
i
n
−
1
4
5
+
s
i
n
−
1
1
3
and
β
=
c
o
s
−
1
4
5
+
c
o
s
−
1
1
3
,
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
.
solve for x the following equations :
(a)
c
o
t
−
1
x
+
s
i
n
−
1
1
√
(
5
)
=
π
4
(b)
2
t
a
n
−
1
(
c
o
s
x
)
=
t
a
n
t
a
n
−
1
(
2
c
o
s
e
c
x
)
.
(c)
t
a
n
(
c
o
s
−
1
x
)
=
s
i
n
(
c
o
t
−
1
1
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
.
Using the principal values, express the following as a single angle :
3
t
a
n
−
1
(
1
2
)
+
2
t
a
n
−
1
(
1
5
)
+
s
i
n
−
1
142
65
√
5
.
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
.
Prove that
(a)
2
t
a
n
−
1
1
5
+
s
e
c
−
1
5
√
2
7
+
2
t
a
n
−
1
1
8
=
π
4
(b)
c
o
s
−
1
12
13
+
2
c
o
s
−
1
√
(
64
65
)
+
c
o
s
−
1
√
(
49
50
)
=
c
o
s
−
1
1
√
2
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