$sin15^o$
$=sin(45^o-30^o)$
$=sin45^o.cos30^o-cos45^o.sin30^o$
$=\dfrac{\sqrt[]{2}}{2}.\dfrac{\sqrt[]{3}}{2}-\dfrac{\sqrt[]{2}}{2}.\dfrac{1}{2}$
$=\dfrac{\sqrt[]{6}-\sqrt[]{2}}{4}$
$cos15^o$
$=cos(45^o-30^o)$
$=cos45^o.cos30^o+sin45^o.sin30^o$
$=\dfrac{\sqrt[]{2}}{2}.\dfrac{\sqrt[]{3}}{2}+\dfrac{\sqrt[]{2}}{2}.\dfrac{1}{2}$
$=\dfrac{\sqrt[]{6}+\sqrt[]{2}}{4}$
$tan15^o$
$=\dfrac{sin15^o}{cos15^o}$
$=\dfrac{\sqrt[]{6}-\sqrt[]{2}}{\sqrt[]{6}+\sqrt[]{2}}$
$cot15^o$
$=\dfrac{cos15^o}{sin15^o}$
$=\dfrac{\sqrt[]{6}+\sqrt[]{2}}{\sqrt[]{6}-\sqrt[]{2}}$
