# How do you find lim costheta/(pi/2-theta) as theta->pi/2 using l'Hospital's Rule?

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l'Hospital's Rule states that if ${\lim}_{x \to c} f \frac{x}{g} \left(x\right) = \frac{0}{0}$ aka. $f \left(c\right) = 0$ and $g \left(c\right) = 0$, then the limit can be written as ${\lim}_{x \to c} \frac{f ' \left(x\right)}{g ' \left(x\right)}$. If you are still in indeterminate form ($\frac{0}{0}$), then you use l'Hospital's Rule again.
${\lim}_{\theta \to \frac{\pi}{2}} \frac{\cos \theta}{\frac{\pi}{2} - \theta} = {\lim}_{\theta \to \frac{\pi}{2}} \frac{- \sin \theta}{- 1} = {\lim}_{\theta \to \frac{\pi}{2}} \sin \theta = \sin \left(\frac{\pi}{2}\right) = 1$