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: $\sin 30^{\circ}$
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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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