Question

Find the value of $2\sin {45}^{\circ }\cos {15}^{\circ }$

• A. $\left(\frac{\sqrt{3}-1}{2}\right)$
• B. $\left(\frac{\sqrt{3}+1}{2}\right)$
• C. $\left(\frac{\sqrt{5}+1}{2}\right)$
• D. $\left(\frac{\sqrt{5}-1}{2}\right)$

Answer 1

The correct option is B $\left(\frac{\sqrt{3}+1}{2}\right)$

$2\sin {45}^o\cos {15}^o=\sin ({45}^o+{15}^o)+\sin ({45}^o-{15}^o)$
$=\sin {60}^o+\sin {30}^o=\frac{\sqrt{3}}{2}+\frac{1}{2}=\frac{\sqrt{3}+1}{2}$