Question

Challenge Time!!!!
$\begin{gathered}\rm\tiny{Given} \\ \tiny\begin{gathered} \sf{ {C = 1 + r \cos( \theta) + \frac{ {r}^{2} \cos(2 \theta) }{2 ! } + \frac{ {r}^{3} \cos( 3\theta) }{3! } + ... }} \\ \end{gathered} \\ \rm\tiny{and} \\ \tiny\begin{gathered} \sf{ {S = r \sin( \theta) + \frac{ {r}^{2} \sin(2 \theta) }{2 ! } + \frac{ {r}^{3} \sin( 3\theta) }{3! } + ... }} \\ \end{gathered} \\ \rm\tiny{Then,\:\:show\:\:that} \\ \tiny\begin{gathered} \sf{ { C } { \frac{d S }{dr} } -{ S } { \frac{d C }{dr} } = ( { C^{2} } + { S ^{2} } ) \sin( \theta) } \\ \end{gathered}\end{gathered}$
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Answer 1

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Answer 2

Answer:

"3" (and any subsequent words) was ignored because we limit queries to 32 words.