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Question
Expand sec x by McLaurin’s theorem considering up to x4 term.
Solution
Let y = sec 𝑥
y = `1/ (cosx)`
`y=1/(1-x^2/(2!)+x^3/(3!).......`
`y=(1-x^2/(2!)+x^3/(3!)-...)^(-1)`
`y=1-((-x^2)/2+x^4/24)+((-x^2)/2+...)^2+...`
`y=1+x^2/2-x^4/24+x^4/4+.......`
`therefore y=1+x^2/2+5x^4/24+.......`
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