Evaluate $ \lim=?iso-8859-1?Q?=5F{x\rightarrow{\frac\pi2_}}_?=(\sec(x) \tan(x))^{\cos(x)}$ without L'Hôpital's rule – math.stackexchange.com

Evaluate $ \lim_{x\rightarrow{\frac\pi2 }} (\sec(x) \tan(x))^{\cos(x)}$
without L'Hôpital's rule – math.stackexchange.com

I have tried changing limit to $\lim_{x\rightarrow0}$ and use some
trigonometry identity ($\sin^2(x)+\cos^2(x) = 1$ and $\sin (x+\pi/2) =
\cos(x)$) but doesn't work I have no idea on how to do this …