1-sin²10=cos²10
所以原式=(2sin50+sin10+√3sin10*sin10/cos10)*cos10
=2sin50cos10+sin10cos10+√3sin²10
=2sin50cos10+1/2*sin20+√3(1-cos20)/2
=2sin50cos10+1/2*sin20-√3/2cos20+√3/2
=2sin50cos10+sin20cos60-cos20sin60+√3/2
=2sin50cos10+sin(20-60)+√3/2
=2sin50cos10-sin40+√3/2
=2sin50cos10-sin(50-10)+√3/2
=2sin50cos10-sin50cos10+cos50sin10+√3/2
=sin50cos10+cos50sin10+√3/2
=sin(50+10)+√3/2
=sin60+√3/2
=√3