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Question
Mathematics
The value of the determinant |sin2(x+(3π/2))&sin 2(x+(5π/2))&sin2 (x+(7π/2)) sin(x+(3π/2))&sin(x+(5π/2))&sin(x+(7π/2)) sin(x-(3π/2))&sin(x-(5π/2))&sin(x+(7π/2))| is
Q. The value of the determinant
∣
∣
s
i
n
2
(
x
+
2
3
π
)
s
in
(
x
+
2
3
π
)
s
in
(
x
−
2
3
π
)
s
i
n
2
(
x
+
2
5
π
)
s
in
(
x
+
2
5
π
)
s
in
(
x
−
2
5
π
)
s
i
n
2
(
x
+
2
7
π
)
s
in
(
x
+
2
7
π
)
s
in
(
x
+
2
7
π
)
∣
∣
is
1915
264
Determinants
Report Error
A
1
B
2
C
3
D
0
Solution:
Apply
C
3
→
C
3
−
C
1
∣
∣
s
i
n
2
(
x
+
2
3
π
)
s
in
(
x
+
2
3
π
)
s
in
(
x
−
2
3
π
)
s
i
n
2
(
x
+
2
5
π
)
s
in
(
x
+
2
5
π
)
s
in
(
x
−
2
5
π
)
s
in
(
2
x
+
5
π
)
s
in
(
2
π
)
2
cos
(
x
+
2
5
π
)
s
in
(
π
)
2
cos
(
x
−
2
5
π
)
s
in
(
−
π
)
∣
∣
=
0
∴
All elements of
C
3
are zero