(1/cos80°)(3/sin²40-1/cos²40)
＝(1/cos80°)(√3/sin40°+1/cos40°)(√3/sin40°-1/cos40°)
＝(1/cos80°)·[(√3cos40°+sin40°)/sin40°cos40°]·[(√3cos40°-sin40°)/sin40°cos40°]
＝(1/cos80°)·[4sin(40°+60°)/sin80°]·[4sin(60°-40°)/sin80°]
＝(1/cos80°)(4sin100°/sin80°)·(4sin20°/sin80°)
＝(1/cos80°)·(4sin80°/sin80°)·(4sin20°/sin80°)
＝32sin20°/sin160°
＝32sin20°/sin20°
＝32.