The value of limh→0(√3sinπ6+h-cosπ6+h)/(√3h√3cosh-sinh) is :

Correct answer: (C) 2/3. L=limh→0(√312cosh+√32sinh-√32cosh-sinh)/2√3h√3 L=limh→02sinh/3h ⇒L=2/3

Q34 / 90 · JEE Main 2021 (26 Feb Shift 1) · Mathematics

The value of $\lim_{h \to 0} \{\frac{\sqrt{3} \sin (\frac{π}{6} + h) - \cos (\frac{π}{6} + h)}{\sqrt{3} h (\sqrt{3} \cos h - \sin h)}\}$ is :

L = \lim_{h \to 0} (\frac{\sqrt{3} (\frac{1}{2} \cos h + \frac{\sqrt{3}}{2} \sin h) - (\frac{\sqrt{3}}{2} \cos h - \frac{\sin h}{2})}{(\sqrt{3} h) (\sqrt{3})})

$L = \lim_{h \to 0} \frac{2 \sin h}{3 h}$

$\Rightarrow L = \frac{2}{3}$

Hence, the correct answer is option: 'C'.