求sin²20+cos²80+根号三sin²20cos80的值

题目

求sin²20+cos²80+根号三sin²20cos80的值

答案

sin20²+cos²80+√3sin20cos80=(1-cos40)/2+(1+cos160)/2+√3/2(sin100-sin60)=1-1/2cos40-1/2cos20-3/4+√3/2sin100=1/4-1/2(cos40+cos20+√3/2sin80=1/4-cos10cos30+√3/2sin80=1/4-√3/2cos10+√3/2sin8...