sin²13°+cos²17°-sin13°cos17°=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 07:50:38
![sin²13°+cos²17°-sin13°cos17°=?](/uploads/image/z/2496887-71-7.jpg?t=sin%26%23178%3B13%C2%B0%EF%BC%8Bcos%26%23178%3B17%C2%B0%EF%BC%8Dsin13%C2%B0cos17%C2%B0%3D%3F)
sin²13°+cos²17°-sin13°cos17°=?
sin²13°+cos²17°-sin13°cos17°=?
sin²13°+cos²17°-sin13°cos17°=?
sin²13°+cos17°-sin13°cos17°
=(1-cos26°)/2+(1+cos26°)/2-sin13°cos17°
=1+(cos26°-cos34°)/2-sin13°cos17°
=1-sin[(26°+34°)/2]sin[(26°-34°)/2]-[sin(13°+17°)+sin(13°-17°)]/2
(积化和差公式,和差化积公式)
=1-sin30°sin4°-(sin30°-sin4°)/2
=1-(1/2)sin4°-1/4+(1/2)sin4°
=3/4
cos²17°=sin²73°=sin²107°
即sin²13°+sin²107°-sin13°sin107°=?
根据正弦定理即是2rsin13 2rsin107 2rsin60的三角形
(2rsin13 )²+(2rsin107)²-2(2rsin13 )*(2rsin107)*cos...
全部展开
cos²17°=sin²73°=sin²107°
即sin²13°+sin²107°-sin13°sin107°=?
根据正弦定理即是2rsin13 2rsin107 2rsin60的三角形
(2rsin13 )²+(2rsin107)²-2(2rsin13 )*(2rsin107)*cos60=( 2rsin60)²
即sin²13°+sin²107°-sin13°sin107°=3/4
收起
sin²13°+cos17°-sin13°cos17°
=(1-cos26°)/2+(1+cos34°)/2-sin13°cos17°
=1-(cos26°-cos34°)/2-sin13°cos17°
=1+sin[(26°+34°)/2]sin[(26°-34°)/2]-[sin(13°+17°)+sin(13°-17°)]/2
(积化和差公式,和差化...
全部展开
sin²13°+cos17°-sin13°cos17°
=(1-cos26°)/2+(1+cos34°)/2-sin13°cos17°
=1-(cos26°-cos34°)/2-sin13°cos17°
=1+sin[(26°+34°)/2]sin[(26°-34°)/2]-[sin(13°+17°)+sin(13°-17°)]/2
(积化和差公式,和差化积公式)
=1-sin30°sin4°-(sin30°-sin4°)/2
=1-(1/2)sin4°-1/4+(1/2)sin4°
=3/4
收起