Show that \( y=\sin (\sin x) \) is a solution of the differential equation \[ \frac{d^{2} y}{d x...

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Show that \( y=\sin (\sin x) \) is a solution of the differential equation
\[
\frac{d^{2} y}{d x^{2}}+\tan x \frac{d y}{d x}+y \cos ^{2} x=0 .
\]
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