If $A = 30^{o}$ , verify that
$sin 2 A = 2 sin A cos A$

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Solution

If $A = 30^{o}$
$sin 2 A = 2 sin A cos A$
Putting $A = 30^{o}$ in $L . H . S$
$sin 2 A = sin 2 (30^{o})$
$= sin 60^{o}$
$= \frac{\sqrt{3}}{2}$
In $R . H . S$ ,putting $A = 30^{o}$ ,
$2 sin A cos A = 2 sin 30^{o} cos 30^{o}$
$= 2 (\frac{1}{2} \times \frac{\sqrt{3}}{2})$
$\Rightarrow 2 \times \frac{\sqrt{3}}{4}$
$\Rightarrow \frac{\sqrt{3}}{2}$
$\Rightarrow L . H . S = R . H . S = \frac{\sqrt{3}}{2}$

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