Question

Find the value of $2sin15^{\circ}\cdot cos75^{\circ}$.

• A. $\frac{\left(2+\sqrt{3}\right)}{2}$
• B. $1$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{2-\sqrt{3}}{2}$

Answer 1

Answer: (D)

We have,
$2sin15^{\circ}\, cos75^{\circ} = sin\left(15^{\circ} + 75^{\circ}\right) + sin\left(15^{\circ} - 75^{\circ}\right)$
$=sin90^{\circ}-sin60^{\circ}=\frac{2-\sqrt{3}}{2}$