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Mathematics
Mathematics
Problem
If
0
<
θ
<
π
2
0 < \theta < \frac{\pi}{2}
0
<
θ
<
2
π
,
x
=
∑
n
=
0
∞
cos
2
n
θ
x = \sum_{n=0}^{\infty} \cos^{2n} \theta
x
=
∑
n
=
0
∞
cos
2
n
θ
,
y
=
∑
n
=
0
∞
sin
2
n
θ
y = \sum_{n=0}^{\infty} \sin^{2n} \theta
y
=
∑
n
=
0
∞
sin
2
n
θ
and
z
=
∑
n
=
0
∞
cos
2
n
θ
⋅
sin
2
n
θ
z = \sum_{n=0}^{\infty} \cos^{2n} \theta \cdot \sin^{2n} \theta
z
=
∑
n
=
0
∞
cos
2
n
θ
⋅
sin
2
n
θ
, then show
x
y
z
=
x
y
+
z
.
xyz = xy + z.
x
y
z
=
x
y
+
z
.
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