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Byju's Answer
Standard IX
Mathematics
Equilateral and Isosceles Triangle Properties
Let fnx = 1...
Question
Let
f
n
(
x
)
=
(
1
/
n
)
(
sin
n
x
+
cos
n
x
)
for
n
=
1
,
2
,
3
,
.
.
.
.
then
f
4
(
3
π
/
8
)
−
f
6
(
3
π
/
8
)
is equal to
A
2
/
(
√
2
+
1
)
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B
1
/
12
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C
4
/
(
√
3
−
1
)
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D
1
/
8
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Solution
The correct option is
A
2
/
(
√
2
+
1
)
f
n
(
x
)
=
(
1
n
)
(
sin
n
x
+
cos
n
x
)
f
4
(
x
)
−
f
6
(
x
)
=
(
1
4
)
(
cos
4
x
+
sin
4
x
)
−
1
6
(
cos
6
x
+
sin
6
x
)
........
(
1
)
using
a
3
+
b
3
=
(
a
+
b
)
(
a
2
+
b
2
−
a
b
)
(
cos
2
x
)
3
+
(
sin
2
x
)
3
=
(
sin
2
x
+
cos
2
x
)
(
sin
4
+
cos
4
x
−
sin
2
x
⋅
cos
2
x
)
..........
(
2
)
sin
2
x
+
cos
2
x
=
1
........
(
3
)
put eq
(
2
)
& eq
(
1
)
f
4
(
x
)
−
f
6
(
x
)
=
1
4
(
cos
4
x
+
sin
4
x
)
−
1
6
(
sin
4
x
+
cos
4
x
−
sin
2
x
cos
2
x
)
=
2
24
(
cos
4
x
+
sin
4
x
)
+
1
6
sin
2
x
cos
2
x
=
1
12
(
cos
4
x
+
sin
4
x
+
2
sin
2
x
cos
2
x
)
=
1
12
(
sin
2
x
+
cos
2
x
)
2
=
1
12
Independent of x.
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Similar questions
Q.
If
f
n
(
x
)
=
1
n
(
cos
n
x
+
sin
n
x
)
,
for
n
=
1
,
2
,
3
,
.
.
.
.
,
then
f
4
(
x
)
−
f
6
(
x
)
is equal to
Q.
Assertion :Let
2
1
/
14
.4
1
/
8
.8
1
/
16
.16
1
/
32
.
.
.
∞
=
2
x
then the value of
x
is equal to 1. Reason: The sum of series
1
4
+
2
8
+
3
16
+
4
32
=
.
.
.
∞
is equal to 1.
Q.
Evaluate:
lim
n
→
∞
(
1
3
+
2
3
+
3
3
+
.
.
.
+
n
3
)
(
1
4
+
2
4
+
3
4
+
.
.
.
+
n
4
)
(
1
8
+
2
8
+
3
8
+
.
.
.
+
n
8
)
Q.
For a positive integer
n
, let
S
(
n
)
=
1
+
1
2
+
1
4
+
1
8
+
.
.
.
.
.
+
1
2
n
. Then
S
100
>
100
.
Q.
From the sets given below, select equal set:
A
=
{
2
,
4
,
8
,
12
}
,
B
=
{
1
,
2
,
3
,
4
}
,
C
=
{
4
,
8
,
12
,
14
}
,
D
=
{
3
,
1
,
4
,
2
}
E
=
{
−
1
,
1
}
,
F
=
{
0
,
a
}
,
G
=
{
−
1
,
1
}
,
H
=
{
0
,
1
}
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