Question

The value of $\cos {15}^{\circ }$ is _____________.

• A. $\frac{\sqrt{3}+1}{2\sqrt{2}}$
• B. $\frac{2+\sqrt{3}}{4}$
• C. $\frac{\sqrt{3}-1}{2\sqrt{2}}$
• D. $\frac{\sqrt{3}+1}{4}$

Answer 1

Answer: (A)

$\frac{\sqrt{3}+1}{2\sqrt{2}}$

$cos{15}^{\circ }=cos({45}^{\circ }-{30}^{\circ })$

$=cos{45}^{\circ }cos{30}^{\circ }+sin{45}^{\circ }sin{30}^{\circ }$

$=\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}$

$=\frac{\sqrt{3}+1}{2\sqrt{2}}$