How do you find the limit as x approaches (pi/2)- of (tanx)^x ?

I graphed that function, and it looks like +infinity to me.

tan( pi/2) is infinite,and infinity to any finite power is infinite,

Let y= (tan x)^x
ln y = x ln (tan x)

= lim x-->pi/2 x * lim x-->pi/2 ln (tan x)
= (pi/2)* ∞
= ∞

ln y -->∞
y --> e^∞ = ∞

Infinity
To see how things are going note that pi/2 ~ 1.57079632679
So, x = 1.57079 is near pi/2
(tanx)^x ~ 15408148753.6

there may well be a better and more formal way to calculate the limit