Evaluate \( \lim _{x \rightarrow \frac{\pi}{6}} \frac{2 \sin x}{\sqrt{3} \sec x-\cot ^{2} x} \)
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Step 1: Identify the trigonometric values at \( x = \frac{\pi}{6} \): \[ \sin \left( \frac{\pi}{6} \right) = \frac{1}{2}, \quad \sec \left( \frac{\pi}{6} \right) = \frac{2}{\sqrt{3}}, \quad \cot \left( \frac{\pi}{6} \right) = \sqrt{3} \] Show more…
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