2sin130°+sin100°（1+√3tan370°）
=2sin50°+cos10°(1+√3tan10°)
=2sin50°+(cos10°+√3sin10°)
=2sin50°+2sin(10°+30°)
=2sin50°+2cos50°
=2√2sin(50°+45°)
=2√2cos5°
又1+cos10°=2（cos5°）^2 ∴√(1+cos10°)=√2cos5°
∴ [2sin130°+sin100°（1+√3tan370°）]÷√(1+cos10°)=(2√2cos5°)/(√2cos5°)=2