Question

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

Answer 1

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+.........`