First slide

Trignometry

Question

If $A = 60^{o}, then the value of \sin (2 A) is equal to$

Moderate

A

$\frac{\sqrt{3}}{2}$
B

$\frac{\sqrt{2}}{1}$
C

$\frac{\sqrt{5}}{4}$
D

$\frac{\sqrt{8}}{7}$

Solution

Since sin $(2 A) = 2 \sin A \cos A$
So for $A = 60^{0},$ we have
sin $(2 A) = 2$ sin A cos A = 2 sin (60^o)cos (60⁰)
$\Rightarrow$ sin $(2 A) = 2 (\frac{\sqrt{3}}{2}) (\frac{1}{2}) = \frac{\sqrt{3}}{2}$

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