# Trigonometric Limit without L'hospital (0/0 kind): <munder> <mo form="prefix">lim <mro

Trigonometric Limit without L'hospital (0/0 kind):
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Hint. We have that

Then use the fact that
$\mathrm{cos}\left(t+\frac{\pi }{6}\right)=\mathrm{cos}\left(t\right)\mathrm{cos}\left(\frac{\pi }{6}\right)-\mathrm{sin}\left(t\right)\mathrm{sin}\left(\frac{\pi }{6}\right)=\frac{\sqrt{3}}{2}\cdot \mathrm{cos}\left(t\right)-\frac{1}{2}\cdot \mathrm{sin}\left(t\right).$