√3sin45°÷sin75°=√3sin45°÷sin(45°+30°)
=√3sin45°÷[sin45°cos30°+cos45°sin30°]
=√3sin45°÷(√6/4 +√2/4)
=√6/2 ÷ [(√6+√2)/4]
=√6*2/(√6+√2)=√6(√6-√2)/2=3-√3