Question

Find the exact value of $cos{15}^{\circ }$.

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

Answer 1

The correct option is A $\frac{\sqrt{3}+1}{2\sqrt{2}}$

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