Answer
$y=tan(x+\frac{\pi}{2})$
Work Step by Step
The period of $y=tan(x)$ is $\pi$; thus $tan(x-\frac{\pi}{2})=tan(x+\frac{\pi}{2}-\pi)=tan(x+\frac{\pi}{2})$. We can identify that the graph fits the equation $y=tan(x+\frac{\pi}{2})$
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