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Is  $\dfrac{\sin 30^{\circ} \times \tan 60^{\circ}}{\tan 30^{\circ} \times \cos 60^{\circ}}=3$
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The two sides are not equal.

Left Hand Side:

Factorization
$\frac{\sin{\left(\frac{\pi}{6} \tan{\left(\frac{\pi}{3} \right)} \right)}}{\tan{\left(\frac{\pi}{6} \cos{\left(\frac{\pi}{3} \right)} \right)}}$

Result
$\frac{\sin{\left(\frac{\sqrt{3} \pi}{6} \right)}}{2 - \sqrt{3}}$

Numerical
$2.93935254788098$

Simplification
$\sqrt{3} \sin{\left(\frac{\sqrt{3} \pi}{6} \right)} + 2 \sin{\left(\frac{\sqrt{3} \pi}{6} \right)}$

So $LHS\neq RHS$

by Diamond (89,036 points)

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