Question:
The value of $\lim _{h \rightarrow 0}\left\{\frac{\left.\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)^{-\cos \left(\frac{\pi}{6}+h\right.}\right)}{\sqrt{3} h(\sqrt{3} \cosh -\sinh )}\right\}$ is:
Correct Option: , 3
Solution:
$\lim _{h \rightarrow 0} 2 \times 2\left\{\frac{\sin \left(\frac{\pi}{6}+h-\frac{\pi}{6}\right)}{2 \sqrt{3 h}\left(\cos \left(h+\frac{\pi}{6}\right)\right.}\right\}$
$=\frac{2}{\sqrt{3}} \times \frac{2}{\sqrt{3}}=\frac{4}{3}$
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