Question : Find the value of $\sin 47^{\circ} \cos 33^{\circ} -\cos 43^{\circ} \sin 57^{\circ}$.
Option 1: –1
Option 2: 1
Option 3: 0
Option 4: $\frac{1}{2}$
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Correct Answer: 0
Solution :
$\sin 47^{\circ} \cos 33^{\circ} -\cos 43^{\circ} \sin 57^{\circ}$
= $\sin 47^{\circ} \cos 33^{\circ}-\cos (90^\circ-47^{\circ} )\sin (90^\circ-33^{\circ})$
= $\sin 47^{\circ} \cos 33^{\circ}-\sin 47^{\circ} \cos 33^{\circ}$
= $0$
Hence, the correct answer is 0.
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