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Trigonometry
Question

a. Use the binomial series and the fact that \(\f...

a. Use the binomial series and the fact that \(\frac { d } { d x } \sin ^ { - 1 } x = ( 1 - x ^ { 2 } ) ^ { - 1 / 2 }\)

Answer

\(\left. \begin{array} { l } { \text { (a) } x + \frac { x ^ { 3 } } { 6 } + \frac { 3 x ^ { 5 } } { 40 } + \frac { 5 x ^ { 7 } } { 112 } , \text { radius of convergence } = 1 } \\ { \text { (b) } \frac { \pi } { 2 } - x - \frac { x ^ { 3 } } { 6 } - \frac { 3 x ^ { 5 } } { 40 } - \frac { 5 x ^ { 7 } } { 112 } } \end{array} \right.\)

Solution
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