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Question
Mathematics
cos[tan-1 sin(cot-1x) ] is equal to
Q.
cos
[
t
a
n
−
1
{
s
in
(
co
t
−
1
x
)}]
is equal to
4840
146
Inverse Trigonometric Functions
Report Error
A
x
2
+
3
x
2
+
2
10%
B
x
2
+
1
x
2
+
2
44%
C
x
2
+
2
x
2
+
1
29%
D
None of these
17%
Solution:
We have,
cos
[
t
a
n
−
1
{
s
in
(
co
t
−
1
x
)}]
Let
co
t
−
1
x
=
θ
⇒
co
t
θ
=
x
⇒
s
in
θ
=
1
+
x
2
1
∴
cos
[
t
a
n
−
1
{
s
in
θ
}
]
=
cos
[
t
a
n
−
1
(
1
+
x
2
1
)
]
Again, let
t
a
n
−
1
1
+
x
2
1
=
ϕ
⇒
t
an
ϕ
=
1
+
x
2
1
⇒
cos
ϕ
=
2
+
x
2
1
+
x
2
∴
cos
[
t
a
n
−
1
1
+
x
2
1
]
=
cos
ϕ
=
x
2
+
2
x
2
+
1