先计算sin50(1+√3tan10)的值：
sin50（1+√3tan10）
=sin50[1+√3(sin10/cos10)]
=sin50[(cos10+√3sin10)/cos10]
=sin50[2sin(30+10)/cos10]
=(2sin50sin40)/cos10°
=(2cos40°*sin40°)/cos10°
=sin80°/cos10°
=cos10°/cos10°
=1
所以[cos40+sin50(1+√3tan10)]/sin70√(1+sin50)
=[cos40+1]/[sin70√(1+sin50)]
=(2 cos²20)/[ cos20*√(sin25+cos25)²]
=(2 cos²20)/[ cos20*(sin25+cos25)]
=(2 cos20)/(sin25+cos25)
=(2 cos20)/[√2(sin25+45))
=(2 cos20)/[√2sin70]
=(2 cos20)/[√2cos20]
=√2.