Монгол Бодлогын Сан

Заавар: $$\begin{align*} \cos\alpha+\cos\beta&=\phantom{-}2\cos\dfrac{\alpha+\beta}{2}\cos\dfrac{\alpha-\beta}{2}\\ \cos\alpha-\cos\beta&=-2\sin\dfrac{\alpha+\beta}{2}\sin\dfrac{\alpha-\beta}{2} \end{align*}$$

Бодолт: $$\begin{align*} \text{Илэрх.}&=\cos115^{\circ}-\cos 35^{\circ}+\cos65^{\circ}+\cos 25^{\circ}\\ &=(\cos115^\circ+\cos65^\circ)-(\cos35^\circ-\cos25^\circ)\\ &=2\cdot\cos\dfrac{115^\circ+65^\circ}{2}\cdot\cos\dfrac{115^\circ-65^\circ}{2}+2\cdot\sin\dfrac{35^\circ+25^\circ}{2}\cdot\sin\dfrac{35^\circ-25^\circ}{2}\\ &=2\cdot\cos90^\circ\cdot\cos25^\circ+2\cdot\sin30^\circ\cdot\sin5^\circ\\ &=2\cdot\dfrac12\cdot\sin5^\circ=\sin5^\circ \end{align*}$$