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

Sum

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

#### Solution

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+.........

Concept: Logarithmic Functions
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