What's the limit of $\tan x$ when $x$ aproaches $\pi /2$ by the left?

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To be more specific:

$$\lim_{x\to (\pi/2)^-} \tan x$$

Thanks :)

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1 Answer

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Hint: Write $\tan(x) = \dfrac{\sin x}{\cos x}$ and then take the limit: $$\lim_{x\to \large \frac \pi 2\,^-} \dfrac {\sin x}{\cos x}$$

The numerator approaches $1$ and the denominator approaches $0$, when $x$ is approaching $\pi/2$ from the left. So the limit is $...\,?$

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