Such problems are typical ones that can be solved by applying sum-to-product and product-to-sum formulas: \begin{align*} &\frac{1}{2}\cdot (\cos 10^\circ - \cos 60^\circ) \cdot \sin 85^\circ\\ =\quad &\frac{1}{2}\cdot(\cos 10^\circ \sin 85^\circ - \cos 60^\circ \sin 85^\circ)\\ =\quad&\frac{1}{2}\cdot\cos 10^\circ\sin 85^\circ -\frac{1}{2}\cdot\cos 60^\circ\sin 85^\circ\\ =\quad& \frac{1}{4}(\sin 95^\circ + \sin 75^\circ) - \frac{1}{4}\cdot\sin 85^\circ\\ =\quad&\frac{1}{4}(\sin 85^\circ + \cos 15^\circ) -\frac{1}{4}\cdot\sin 85^\circ\\ =\quad&\frac{1}{4}\cdot\cos 15^\circ\\ =\quad&\frac{\sqrt{6}+\sqrt{2}}{16} \end{align*} While applying sum-product formula is the "usual standard" approach, this problem can also be solved by applying the triple angle formula %%HREF%%2255%% by setting $\alpha$ to $25^\circ$.