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Byju's Answer
Standard XII
Mathematics
Derivative of One Function w.r.t Another
59.The value ...
Question
59.The value of cos inverse (4/5) + tan inverse (3/5) is equal to (1) tan inverse (27/11) (2) sin inverse (11/27) (3) cos inverse (11/27) (4) zero
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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
1
2
+
t
a
n
−
1
1
3
=
π
4
.
(b)
t
a
n
−
1
1
2
+
t
a
n
−
1
1
5
+
t
a
n
−
1
1
8
=
π
4
(c)
t
a
n
−
1
3
4
+
t
a
n
−
1
3
5
−
t
a
n
−
1
8
19
=
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
.
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.
cos
−
1
(
cos
(
−
5
)
)
+
sin
−
1
(
sin
(
6
)
)
−
tan
−
1
(
tan
(
12
)
)
is equal to
(The inverse trigonometric functions take the principal values)
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
.
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