{2sin50°+ sin100°[1 + (√3)tan370°]}/√(1 + cos10°)
= {2sin50°+ cos10°[1 + (√3)tan10°]}/√(1 + cos10°)
= {2sin50°+ [cos10°+ (√3)sin10°]}/√(1 + cos10°)
= {2sin50°+ 2[½cos10°+ ½(√3)sin10°]}/√(1 + cos10°)
= {2sin50°+ 2[sin30°cos10°+ cos30°sin10°]}/√(1 + cos10°)
= {2sin50°+ 2sin40°}/(√2)cos5°
= (√2){sin50°+ sin40°}/cos5°
= (√2)[2sin45°cos5°]/cos5°
= (√2)2sin45°
= (√2)2×(√2)/2
= 2
[此解答万无一失]