Answer
$+\infty$
Work Step by Step
$\displaystyle \tan x=\frac{\sin x}{\cos x}$
You can sketch a unit circle. 0 radians is at (1,0); the positive direction is counterclockwise. $\displaystyle \frac{\pi}{2}$ radians is positioned at $(0,1).$
When $x\displaystyle \rightarrow(\frac{\pi}{2})^{-}$, x is a radian angle measure in the first quadrant, (slightly less than $\displaystyle \frac{\pi}{2} $is on the clockwise side of $\displaystyle \frac{\pi}{2}$) where both sine and cosine are positive.
The numerator, $\sin x\rightarrow 1$, (positive) and the denominator, $\cos x\rightarrow 0$, (positive).
Thus, $\displaystyle \frac{\sin x}{\cos x}=\tan x\rightarrow+\infty$
