化简:[2sin50°+sin10°(1+根号3*tan10°）]*根号sin^280°

[2sin50+sin10(1+根号3*tan10) ]根号（sin^2(80))
= [2sin50+sin10(1+根号3*sin10/cos10) ] sin80
= [2sin50+sin10(1+根号3*sin10/cos10) ] cos10
= 2sin50cos10 + sin10(cos10+根号3*sin10)
= 2sin50cos10 + sin10 { 2( sin30 cos10+cos30 sin10) }
= 2sin50cos10 + sin10 { 2 sin(30+10) }
= 2sin50cos10 + 2sin10 sin40
= 2 {sin50cos10 + sin10 cos(90-40) }
= 2 {sin50cos10 + cos50sin10}
= 2 sin(50+10)
= 2sin60
=2*根号3/2
= 根号3