1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
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
.
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
.
Open in App
Solution
s
i
n
−
1
x
a
=
t
a
n
−
1
x
√
(
a
2
−
x
2
)
∴
T
3
=
t
a
n
−
1
142
31
2
t
a
n
−
1
x
=
t
a
n
−
1
2
x
1
−
x
2
∴
T
2
=
t
a
n
−
1
5
12
3
t
a
n
−
1
x
=
t
a
n
−
1
3
x
−
x
3
1
−
3
x
2
∴
T
1
=
t
a
n
−
1
11
2
∴
E
=
t
a
n
−
1
11
2
+
t
a
n
−
1
5
12
+
t
a
n
−
1
142
31
=
π
+
t
a
n
−
1
11
2
+
5
12
1
−
55
24
+
t
a
n
−
1
142
31
Here
a
b
>
1
and hence
π
+
t
a
n
−
1
(
)
=
π
−
t
a
n
−
1
142
31
+
t
a
n
−
1
142
31
=
π
.
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
2
c
o
s
−
1
(
√
5
3
)
]
(b)
t
a
n
[
2
t
a
n
−
1
(
1
5
)
−
π
4
]
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
.
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
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
.
2
t
a
n
−
1
(
√
a
−
b
a
+
b
t
a
n
θ
2
)
=
c
o
s
−
1
a
c
o
s
θ
+
b
a
+
b
c
o
s
θ
.
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
,
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Parametric Differentiation
MATHEMATICS
Watch in App
Explore more
Parametric Differentiation
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app