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Mathematics
Mathematics
Problem
Which of the following is equivalent to
sin
3
x
cos
5
x
\sin 3x\,\cos 5x
sin
3
x
cos
5
x
? a)
1
2
(
sin
8
x
+
sin
2
x
)
\tfrac12\bigl(\sin 8x+\sin 2x\bigr)
2
1
(
sin
8
x
+
sin
2
x
)
b)
1
2
(
cos
8
x
+
cos
2
x
)
\tfrac12\bigl(\cos 8x+\cos 2x\bigr)
2
1
(
cos
8
x
+
cos
2
x
)
c)
1
2
(
sin
8
x
−
sin
2
x
)
\tfrac12\bigl(\sin 8x-\sin 2x\bigr)
2
1
(
sin
8
x
−
sin
2
x
)
d)
1
2
sin
8
x
\tfrac12\sin 8x
2
1
sin
8
x
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