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Expand in ascending powers of x. cos x,...

Expand in ascending powers of x. cos x,

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`cosx=1/2(e^(is)+e^(-is))=1/2[(1+ix+(i^2x^2)/(2!)+(i^3x^3)/(3!)+...)+(1-ix+(e^2x^2)/(2!)-(i^3x^3)/(3!)+...)]=1/2[2(1-x^2/(2!)+x^4/(4!)-...)]=1-x^2/(2!)+x^4/(4!)-...`
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