[tex]\it \cos\alpha-\cos \beta=-2sin\dfrac{\alpha+\beta}{2}sin\dfrac{\alpha-\beta}{2}\\ \\ \\ \cos20^o-\cos80^o=-2sin\dfrac{20^o+80^o}{2}sin\dfrac{20^o-80^o}{2} =-2\sin50^o\sin(-30^o)=\\ \\ \\ = -2 \sin50^o\cdot\bigg(-\dfrac{1}{2}\bigg)=-2\cdot\bigg(-\dfrac{1}{2}\bigg)sin50^o=+\not2\cdot\dfrac{1}{\not2}\sin50^o=\sin50^o[/tex]
