Answer
$cos(15^o)= \frac{\sqrt{2+\sqrt{3}}}{2}$
Work Step by Step
Remember$\;\;\;\;\;cos(\frac{x}{2})=\pm \sqrt{\frac{1+cos(x)}{2}}$
$cos(15^o)=\pm \sqrt{\frac{1+cos(30^o)}{2}}$
We know $15^o$ in quadrant $I$ so $cos(15^o)$ is positive
$cos(15^o)= \sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}$
$cos(15^o)= \sqrt{\frac{2+\sqrt{3}}{4}}$
$cos(15^o)= \frac{\sqrt{2+\sqrt{3}}}{2}$
