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Tardigrade
Question
Mathematics
If ∫ limits ( cos 8x + 1/ tan 2x - cot 2x) dx = a cos 8x + c , then a =
Q. If
∫
t
a
n
2
x
−
c
o
t
2
x
c
o
s
8
x
+
1
d
x
=
a
cos
8
x
+
c
,
then
a
=
7997
196
COMEDK
COMEDK 2015
Integrals
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A
−
16
1
23%
B
8
1
21%
C
16
1
45%
D
−
8
1
11%
Solution:
L.H.S =
∫
t
a
n
2
x
−
c
o
t
2
x
c
o
s
8
x
+
1
d
x
∫
(
s
i
n
2
x
c
o
s
2
x
s
i
n
2
2
x
−
c
o
s
2
2
x
)
2
c
o
s
2
4
x
d
x
=
−
∫
(
c
o
s
2
2
x
−
s
i
n
2
2
x
)
c
o
s
2
4
x
(
2
s
i
n
2
x
c
o
s
2
x
)
d
x
=
−
∫
c
o
s
4
x
c
o
s
2
4
x
×
s
i
n
4
x
d
x
=
−
2
1
∫
2
sin
4
x
cos
4
x
d
x
=
−
2
1
∫
sin
8
x
d
x
=
2
1
×
8
c
o
s
8
x
+
c
Now,
2
1
8
c
o
s
8
x
+
c
=
a
cos
8
x
+
c
∴
a
=
16
1