Question

Find that
$\cos {15}^{\circ }$

Answer 1

$\cos {15}^{\circ }$

${15}^{\circ }={45}^{\circ }-{30}^{\circ }$

$\therefore \cos \left(15\right)=\cos (45-30)$

$\Rightarrow \cos 45\cos 30+\sin 45\sin 30$

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

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