化简：[sin50°+cos40°(1+根号3tan10°)]/sin²70°

题目

化简：[sin50°+cos40°(1+根号3tan10°)]/sin²70°

答案

cos40度(1+根号3tan10度)
=2(cos40/cos10)((1/2)cos10+((根号3)/2)sin10)
=2(cos40/cos10)sin(10+30)
=sin80/cos10
=1
所以:
[sin50°+cos40°(1+根号3tan10°)]/sin²70°
=[sin50度+cos40度(1+根号3tan10度)]/cos²20°
=(1+sin50)/(cos20)^2
=(1+sin50)/[(1+cos40)/2]
=2(1+sin50)/(1+cos40)
=2(1+cos40)/(1+cos40)
=2