Question : The value of $\left(\sin 30^{\circ} \cos 60^{\circ}-\cos 30^{\circ} \sin 60^{\circ}\right)$ is equal to:
Option 1: $-\cos 30^{\circ}$
Option 2: $-\sin 30^{\circ}$
Option 3: $\cos 30^{\circ}$
Option 4: $\sin 30^{\circ}$
Correct Answer: $-\sin 30^{\circ}$
Solution :
Given: $\left(\sin 30^{\circ} \cos 60^{\circ}-\cos 30^{\circ} \sin 60^{\circ}\right)$
$=\frac{1}{2}×\frac{1}{2}-\frac{\sqrt3}{2}×\frac{\sqrt3}{2}$
$=\frac{1}{4}-\frac{3}{4}$
$=-\frac{1}{2}$
$=-\sin 30^{\circ}$
Hence, the correct answer is $-\sin 30^{\circ}$.
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