How to obtain the taylor series of $\frac{1}{\cos x}$ up to the 6th order term?

Question

How to obtain the taylor series of $\frac{1}{\cos x}$ up to the 6th order term?

As far I know, we should use the taylor series of $\cos x$.

Answer 1

HINT

Let use

• $\cos x = 1-\frac12 x^2 + \frac 1 {4!} x^4 - \frac 1 {6!} x^6+o(x)$

and

• $(1+x)^a=1+ax+\frac12 a(a-1)x^2+\frac16 a(a-1)(a-2)x^3+o(x^3)$