Find-the-series-for-cosx-Hence-deduce-series-sin-2-x-and-show-that-if-x-is-small-sin-2-x-x-2-cosx-x-4-1-6-x-2-360-approximately-Help-

Question Number 185036 by Mastermind last updated on 16/Jan/23

Find the series for cosx . Hence,

deduce series \sin^{2} x and show that,

if x is small, \frac{\sin^{2} x - x^{2} cosx}{x^{4}} = \frac{1}{6} + \frac{x^{2}}{360}

approximately .

Help!

Answered by aba last updated on 16/Jan/23

\cos (x) = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n}}{(2 n)!}

\sin^{2} (x) = \frac{1 - \cos (2 x)}{2} = \frac{1}{2} [1 - \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} {(2 x)}^{2 n}}{(2 n)!}]

Facebook Tweet Pin