求证1/sin50°+4sin10°=2

1/sin50°+4sin10°=(1+4sin10°sin50°)/sin50°=[1+2cos(50°-10°)-2cos(50°+10°)]/sin50°=2cos40°/sin50°=2sin50°/sin50°=22sinαsinβ=cos(α-β)-cos(α+β)公式推导：cos(α-β)=cosαcosβ+sinαsinβ ①cos(α+β)=cosαcosβ-sinαsinβ ②①-②：cos(α-β)-cos(α+β)=2sinαsinβ