本题目来源于试卷: Maclaurin Series，类别为 IB数学
[问答题]
Let the Maclaurin serioaf/qaxa v8n 5(l3c+ q)ad:eyy+ x)yuiqa:zc /dsaxz: sq3 a9 9cgw,+es for $\cot x$ be
$\cot x=\frac{a_{1}}{x}+a_{2} x+a_{3} x^{3}+\cdots$
where $a_{1}$,$ a_{2} $ and $a_{3} $ are non zero constants.
1. Find the series for $\csc ^{2} x$ , in terms of $a_{1}$,$ a_{2} $ and $a_{3} $, up to and including the $x^{2}$ term
a. by differentiating the above series for $\cot x$ ;
b. by using the relationship $\csc ^{2} x=1+\cot ^{2} x$ .
2. Hence, by comparing your two series, determine the values of $a_{1}$,$ a_{2} $ and $a_{3} $ .
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