Question

Is  \(\dfrac{\sin 30^{\circ} \times \tan 60^{\circ}}{\tan 30^{\circ} \times \cos 60^{\circ}}=3\)

Answer 1

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 $LHS\neq RHS$