Question : What is the value of $\cos45° \sin15°$?
Option 1: $\frac{(\sqrt{3}-1)}{2}$
Option 2: $\frac{(\sqrt{3}-1)}{4}$
Option 3: $(\sqrt{3}+1)$
Option 4: $2 \sqrt{3}-1$
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Correct Answer: $\frac{(\sqrt{3}-1)}{4}$
Solution : $\cos 45° \sin 15°$ $=\frac{1}{2}[2\cos 45° \sin 15°]$ We know, $2\cos A\sin B=\sin(A+B)-\sin(A-B)$ $=\frac{1}{2}[\sin(45°+15°)-\sin(45°-15°)]$ $=\frac{1}{2}[\sin(60°)-\sin(30°)]$ $=\frac{1}{2}×[\frac{\sqrt3}{2}-\frac{1}{2}]$ $=\frac{1}{2}×\frac{\sqrt{3}−1}{2}$ $=\frac{\sqrt3-1}{4}$ Hence, the correct answer is $\frac{\sqrt3-1}{4}$.
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