${lim}_{x \to \frac{π}{2}} \frac{t a n 2 x}{x - \frac{π}{2}}$

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Solution

$l i m_{x \to \frac{π}{2}} \frac{t a n 2 x}{x - \frac{π}{2}}$

$= l i m_{x \to \frac{π}{2}} \frac{2 s e c^{2} 2 x}{1}$

$= 2 s e c^{2} π$

$= 2 (- 1)^{2} = 2$

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