Question

Simplifique a expressão cos 70° + cos 10°/sen 110° + sen 50°

Answer 1

$\mathrm{\dfrac{\cos{70\º+\cos{10\º}}}{\sin{110\º}+\sin{50\º}}=\dfrac{2\cos{\bigg(\dfrac{70\º+10\º}{2}\bigg)}\cos{\bigg(\dfrac{70\º-10\º}{2}\bigg)}}{2\sin{\bigg(\dfrac{110\º+50\º}{2}\bigg)}\cos{\bigg(\dfrac{110\º-50\º}{2}\bigg)}}=}\\\\\\ \mathrm{=\dfrac{\cos{\bigg(\dfrac{80\º}{2}\bigg)}\cos{\bigg(\dfrac{60\º}{2}\bigg)}}{\sin{\bigg(\dfrac{160\º}{2}\bigg)\cos{\bigg(\dfrac{60\º}{2}\bigg)}}}=\dfrac{\cos{40\º}}{\sin{80\º}}=\dfrac{\cos{40\º}}{\sin{\big(2.40\º\big)}}=}$

$\mathrm{=\dfrac{\cos{40\º}}{2\sin{40\º}\cos{40\º}}=\dfrac{1}{2}.\dfrac{1}{\sin{40\º}}=\mathbf{\bigg\| \ \dfrac{\csc{40\º}}{2}}\ \bigg\|}$