What is the value of cos15° - cos165°?

Answer: Option C

$$\begin{array}{l}\cos 15^{\circ }-\cos 165^{\circ }\\ =\cos 15^{\circ }-\cos \left({180}^{\circ }-{15}^{\circ }\right)\\ =\cos 15^{\circ }+\cos 15^{\circ }\\ =2\cos 15^{\circ }\\ =2\left(\frac{\sqrt{3}+1}{2\sqrt{2}}\right)\\ =\frac{\sqrt{3}+1}{\sqrt{2}}\\ \mathbf{Note}:\\ \left[\begin{array}{l}\cos 15^{\circ }=\cos \left({45}^{\circ }-{30}^{\circ }\right)\\ =\cos 45^{\circ }\cos 30^{\circ }+\sin 45^{\circ }\sin 30^{\circ }\\ =\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2}+\frac{1}{\sqrt{2}}\times \frac{1}{2}\\ =\frac{\sqrt{3}+1}{2\sqrt{2}}\end{array}\right]\end{array}$$