[2sin50°+sin80°(1+√3tan10°)]/cos5°
=[2sin50°+cos10°(cos10°+√3sin10°)/cos10°]/cos5°
=[2sin50°+2(1/2*cos10°+√3/2*sin10°)]/cos5°
=[2sin50°+2(cos60°*cos10°+sin60°*sin10°)]/cos5°
=[2sin50°+2cos50°]/cos5°
=2√2*(sin50°*cos45°+cos50°*sin45°)/cos5°
=2√2sin95°/cos5°
=2√2cos5°/cos5°
=2√2