化简{2sin50+sin10(1+根号3*tan10)}*根号sin²80

问题描述:

化简{2sin50+sin10(1+根号3*tan10)}*根号sin²80

原式=(2sin50+sin10+根号3*sin10*tan10)sin80
=2sin50*cos10+根号3*sin10*sin10
=sin(50-10)+sin(50+10)+根号3/2*(1-cos20)
=1/2*(sin40-sin80)+根号3