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Theorems on Integration

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Question

Show that $\frac{{2 t a n 30}^{o}}{1 - {t a n}^{2} 30^{o}} = \sqrt{3}$

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Solution

L.H.S $= \frac{2 tan 30^{o}}{1 - {tan}^{2} 30^{o}}$
$= tan 2 (30^{o})$ $[∵ tan 2 α = \frac{2 tan α}{1 - {tan}^{2} α}]$
$= tan 60^{o}$
$= \sqrt{3} =$ R.H.S.

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