Answer
$$\lim_{x\to(-\pi/2)^+}\sec x=\infty$$
Work Step by Step
$$A=\lim_{x\to(-\pi/2)^+}\sec x=\lim_{x\to(-\pi/2)^+}\frac{1}{\cos x}$$
As $x\to(-\pi/2)^+$, $\cos x$ approaches $\cos(-\pi/2)=0$ from the right, where $\cos x\gt0$.
($x\to(-\pi/2)^+$ are values of $x$ like $-\pi/3, -\pi/4$, etc. and all these values give $\cos x$ positive values)
Therefore, $1/\cos x$ will approach $\infty$. In other words,
$$A=\infty$$
