求sin^220度+cos^250度+sin20度cos50度的值如标题
展开全部
sin²20º+cos²(30º+20)º+sin20ºcos(30º+20º)
=sin²20º+(cos30°cos20°-sin30°sin20°)²+sin20º(cos30°cos20°-sin30°sin20° )
= sin²20°+[(3/4)cos²20°+(1/4)sin²20°-(√3/2)sin20°cos20°]+(√3/2)sin20°cos20°-(1/2)sin²20°
= (1+1/4-1/2)sin²20°+(3/4)cos²20°+(√3/2-√3/2)sin20°cos20°
= (3/4)sin²20°+(3/4)cos²20°
= (3/4)(sin²20°+cos²20°)
= 3/4
=sin²20º+(cos30°cos20°-sin30°sin20°)²+sin20º(cos30°cos20°-sin30°sin20° )
= sin²20°+[(3/4)cos²20°+(1/4)sin²20°-(√3/2)sin20°cos20°]+(√3/2)sin20°cos20°-(1/2)sin²20°
= (1+1/4-1/2)sin²20°+(3/4)cos²20°+(√3/2-√3/2)sin20°cos20°
= (3/4)sin²20°+(3/4)cos²20°
= (3/4)(sin²20°+cos²20°)
= 3/4
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询