Através das Fórmulas de Prostaférese, sabemos que:
[tex]\boxed{\sin{\alpha}+\sin{\beta}=2\sin{\bigg(\dfrac{\alpha+\beta}{2}\bigg)}\cos{\bigg(\dfrac{\alpha-\beta}{2}\bigg)}}[/tex]
Assim, é possível transformar a expressão em:
[tex]\dfrac{\sin{80\º}+\sin{20\º}}{\sin{50\º}}=[/tex]
[tex]\dfrac{1}{\sin{50\º}}\bigg[2\sin{\bigg(\dfrac{80\º+20\º}{2}\bigg)}\cos{\bigg(\dfrac{80\º-20\º}{2}\bigg)}\bigg]=[/tex]
[tex]\dfrac{1}{\sin{50\º}}\bigg[2\sin{50\º}\cos{30\º}\bigg]=2\cos{30\º}=[/tex]
[tex]2\bigg(\dfrac{\sqrt{3}}{2}\bigg)=\boxed{\sqrt{3}}[/tex]
Letra B.
