Question
Evaluate the following:
If A = 45°, verify that:
$\sin2\text{A}=2\sin\text{A}\cos\text{A}$
If A = 45°, verify that:
$\sin2\text{A}=2\sin\text{A}\cos\text{A}$
✓
Answer
$\text{A}=45^\circ$
$\Rightarrow2\text{A}=2\times45^\circ=90^\circ$
$\sin2\text{A}=\sin90^\circ=1$
$2\sin\text{A}\cos\text{A}=2\sin45^\circ\cos45^\circ$
$=2\times\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}=1$
$\therefore\ \sin2\text{A}=2\sin\text{A}\cos\text{A}$
$\Rightarrow2\text{A}=2\times45^\circ=90^\circ$
$\sin2\text{A}=\sin90^\circ=1$
$2\sin\text{A}\cos\text{A}=2\sin45^\circ\cos45^\circ$
$=2\times\frac{1}{\sqrt{2}}\times\frac{1}{\sqrt{2}}=1$
$\therefore\ \sin2\text{A}=2\sin\text{A}\cos\text{A}$
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