Question
Evaluate the following:
Verify the following:
$\sin60^\circ\cos30^\circ-\cos60^\circ\sin30^\circ=\sin30^\circ$
Verify the following:
$\sin60^\circ\cos30^\circ-\cos60^\circ\sin30^\circ=\sin30^\circ$
✓
Answer
$\sin60^\circ\cos30^\circ-\cos60^\circ\sin30^\circ=\sin30^\circ$
$=\Big(\frac{\sqrt{3}}{2}\Big)\times\Big(\frac{\sqrt{3}}{2}\Big)-\Big(\frac12\Big)\times\Big(\frac12\Big)$
$=\frac34-\frac14=\frac24=\frac12$
Also, $\sin30^\circ=\frac{1}{2}$
$\therefore\ \sin60^\circ\cos30^\circ-\cos60^\circ\sin30^\circ$
$=\Big(\frac{\sqrt{3}}{2}\Big)\times\Big(\frac{\sqrt{3}}{2}\Big)-\Big(\frac12\Big)\times\Big(\frac12\Big)$
$=\frac34-\frac14=\frac24=\frac12$
Also, $\sin30^\circ=\frac{1}{2}$
$\therefore\ \sin60^\circ\cos30^\circ-\cos60^\circ\sin30^\circ$
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