求[2sin50度+sin10度(1+根号3*tan10度)]*根号下2倍sin80度的平方 的值

根号6
原式=[2sin50+2sin10/cos10(1/2 *cos10+根号3/2* sin10)]*根号2sin80
=[2sin50+2sin10 cos10 (sin30cos10+cos30 sin10)]*根号2sin80
=(2sin50+2sin10cos10sin40)*根号2sin80 (sin 40=cos 50)
=2/cos10 (sin50 cos10+ sin10 cos 50)*根号2sin80 (sin 80=cos 10)
=2* sin60* 根号2
=根号6