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Byju's Answer
Standard XII
Physics
Antiderivative
x→ 0 limsin 5...
Question
lim
x
→
0
sin
5
x
−
sin
3
x
sin
6
x
−
sin
4
x
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Solution
lim
x
→
0
sin
5
x
−
sin
3
x
sin
6
x
−
sin
4
x
=
lim
x
→
0
sin
5
x
−
sin
3
x
x
sin
6
x
−
sin
4
x
x
=
lim
x
→
0
5
(
sin
5
x
5
x
)
−
lim
x
→
0
3
(
sin
3
x
3
x
)
lim
x
→
0
6
(
sin
6
x
6
x
)
−
lim
x
→
0
4
(
sin
4
x
4
x
)
Now,
lim
x
→
sin
a
x
a
x
=
1
∴
5
−
3
6
−
4
=
1
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0
Similar questions
Q.
Solve the following equations:
(i)
cos
x
+
cos
2
x
+
cos
3
x
=
0
(ii)
cos
x
+
cos
3
x
-
cos
2
x
=
0
(iii)
sin
x
+
sin
5
x
=
sin
3
x
(iv)
cos
x
cos
2
x
cos
3
x
=
1
4
(v)
cos
x
+
sin
x
=
cos
2
x
+
sin
2
x
(vi)
sin
x
+
sin
2
x
+
sin
3
=
0
(vii)
sin
x
+
sin
2
x
+
sin
3
x
+
sin
4
x
=
0
(viii)
sin
3
x
-
sin
x
=
4
cos
2
x
-
2
(ix)
sin
2
x
-
sin
4
x
+
sin
6
x
=
0
Q.
Solve :
sin
2
x
−
sin
4
x
+
sin
6
x
=
0
.
Q.
If
sin
6
x
+
sin
4
x
+
sin
2
x
=
0
, then the value of
x
is
Q.
Let
y
=
cos
x
+
cos
2
x
+
cos
3
x
+
cos
4
x
+
cos
5
x
+
cos
6
x
+
cos
7
x
sin
x
+
sin
2
x
+
sin
3
x
+
sin
4
x
+
sin
5
x
+
sin
6
x
+
sin
7
x
,
then which of the following hold good?
Q.
Let
y
=
e
{
(
sin
2
x
+
sin
4
x
+
sin
6
x
+
…
)
log
e
2
}
satisfy the equation
x
2
−
17
x
+
16
=
0
,
where
0
<
x
<
π
2
.
Then match the correct value of
List I
from
List II
.
List I
List II
(a)
2
sin
2
x
1
+
cos
2
x
(
p
)
1
(b)
2
sin
x
sin
x
+
cos
x
(
q
)
4
9
(c)
∞
∑
n
=
1
(
cot
x
)
n
(
r
)
2
3
(d)
∞
∑
n
=
1
n
(
cot
x
)
2
n
(
s
)
4
3
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