求sin220°+cos280°+3sin20°cos80°的值．

Question

求sin²20°+cos²80°+√(3)sin20°cos80°的值．

Answer 1

原式=sin²20°+sin²10°+√(3)sin20°cos（60°+20°）
=sin²20°+(1)/(2)（1-cos20°）+(√(3))/(2)sin20°cos20°-(3)/(2)sin²20°，
=(1)/(2)（1-cos20°）+(√(3))/(4)sin40°-(1-cos40°)/(4)
=(1)/(4)-(1)/(2)cos20°+(1)/(2)（(√(3))/(2)sin40°+(1)/(2)cos40°）
=(1)/(4)-(1)/(2)cos20°+(1)/(2)sin70°
=(1)/(4)．
故答案为(1)/(4)．