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Prove that Log ( Sec X ) = 1 2 X 2 + 1 12 X 4 + ... ... ... - Applied Mathematics 1

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प्रश्न

Prove that `log(secx)=1/2x^2+1/12x^4+.........`

योग

उत्तर

Let E = log (sec x)
= - log (cos x)

`=-log[1-(x^2/(2!)-x^4/(4!))]`

`=-[-(x^2/(2!)-x^4/(4!))-1/2(x^2/(2!)-x^4/(4!))+........]`

E = `log(secx)=1/2x^2+1/12x^4+.........`

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Logarithmic Functions
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2017-2018 (June) CBCGS

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