[2sin50+sin10(1+√3*tan10)]sin80
=[2sin50+sin10+√3 *sin10*sin10/cos10]cos10
=2sin50cos10+sin10cos10+√3 *sin10*sin10
=2sin50cos10+2sin10(1/2cos10++√3/2 *sin10)
=2sin50cos10+2sin10sin(30+10)
=2sin50cos10+2sin10sin40
=2(sin50cos10+cos50sin10)
=2sin(50+10)
2sin60
=√3