What is the value of cos 105° ? cos 105°

$\cos 105^{\circ}=\cos \left(60^{\circ}+45^{\circ}\right)$

$=\cos 60^{\circ} \cdot \cos 45^{\circ}$

$-\sin 60^{\circ} \cdot \sin 45^{\circ}$

$[\because \cos (A+B)=\cos A \cos B-\sin A \sin B]$

$=\frac{1}{2} \cdot \frac{1}{\sqrt{2}}-\frac{\sqrt{3}}{2} \cdot \frac{1}{\sqrt{2}}$

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