Deduce-the-power-series-of-sin-2-x-Hence-show-that-if-x-is-small-then-sin-2-x-x-2-cosx-x-4-1-6-x-2-360-

Tinku Tara June 4, 2023 Others 0 Comments

Question Number 31340 by NECx last updated on 06/Mar/18

Deduce the power series of sin^2 x. Hence show that if x is small then (sin^2 x − x^2 cosx)/x^4 =(1/6) − (x^2 /(360))

$${Deduce}\:{the}\:{power}\:{series}\:{of}\:{sin}^{\mathrm{2}} {x}. \\ $$$${Hence}\:{show}\:{that}\:{if}\:{x}\:{is}\:{small}\:{then} \\ $$$$\left({sin}^{\mathrm{2}} {x}\:−\:{x}^{\mathrm{2}} {cosx}\right)/{x}^{\mathrm{4}} =\frac{\mathrm{1}}{\mathrm{6}}\:−\:\frac{{x}^{\mathrm{2}} }{\mathrm{360}} \\ $$

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Deduce-the-power-series-of-sin-2-x-Hence-show-that-if-x-is-small-then-sin-2-x-x-2-cosx-x-4-1-6-x-2-360-

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