Answer
$1+\frac{x^{2}}{2}+\frac{5x^{4}}{24}+...$
Work Step by Step
$y=secx=\frac{1}{cosx}$
$cosx=1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-....$
Plug into the limit to get
$secx=\frac{1}{cosx}=\dfrac{1}{1-\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-....}$
$\approx 1+\frac{x^{2}}{2}+\frac{5x^{4}}{24}+...$
