Question:
The value of
$\lim _{h \rightarrow 0} 2\left\{\frac{\sqrt{3} \sin \left(\frac{\pi}{6}+h\right)-\cos \left(\frac{\pi}{6}+h\right)}{\sqrt{3} h(\sqrt{3} \cosh -\sinh )}\right\}$ is
Correct Option: 1
Solution:
$L=\lim _{h \rightarrow 0} 2\left(\frac{\sqrt{3}\left(\frac{1}{2} \cosh +\frac{\sqrt{3}}{2} \sinh \right)-\left(\frac{\sqrt{3}}{2} \cosh -\frac{\sinh }{2}\right)}{(\sqrt{3} h)(\sqrt{3})}\right)$
$\mathrm{L}=\lim _{\mathrm{h} \rightarrow 0} \frac{4 \sinh }{3 \mathrm{~h}}$
$\Rightarrow \mathrm{L}=\frac{4}{3}$