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Mathematics
Mathematics
Problem
If
y
=
cos
x
+
cos
x
+
cos
x
+
…
∞
y = \sqrt{\cos x + \sqrt{\cos x + \sqrt{\cos x + \dots \infty}}}
y
=
cos
x
+
cos
x
+
cos
x
+
…
∞
, then prove that
d
y
d
x
=
sin
x
1
−
2
y
\frac{dy}{dx} = \frac{\sin x}{1-2y}
d
x
d
y
=
1
−
2
y
s
i
n
x
.
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