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Problems
Mathematics
Mathematics
Problem
There exist constants
a
,
b
,
c
a, b, c
a
,
b
,
c
, and
d
d
d
such that
(
sin
x
)
7
=
a
sin
7
x
+
b
sin
5
x
+
c
sin
3
x
+
d
sin
x
(\sin x)^7 = a \sin 7x + b \sin 5x + c \sin 3x + d \sin x
(
sin
x
)
7
=
a
sin
7
x
+
b
sin
5
x
+
c
sin
3
x
+
d
sin
x
for all angles
x
x
x
. Find
d
d
d
.
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