How do you find the exact value of cos15using the half-angle identity?

1 Answer
Feb 8, 2015

Solution

$\cos {30}^{0} = \frac{\sqrt{3}}{2}$
$\cos \left(2 \cdot {15}^{0}\right) = \frac{\sqrt{3}}{2}$
$2 {\cos}^{2} \left({15}^{0}\right) - 1 = \frac{\sqrt{3}}{2}$
$2 {\cos}^{2} \left({15}^{0}\right) = \frac{\sqrt{3} + 2}{2}$
${\cos}^{2} \left({15}^{0}\right) = \frac{\sqrt{3} + 2}{4}$
$\cos \left({15}^{0}\right) = \frac{\sqrt{\left(\sqrt{3} + 2\right)}}{2}$