sin²20°+cos²50°+sin20°cos50°=__? 能告诉我过程吗?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 06:45:58
![sin²20°+cos²50°+sin20°cos50°=__? 能告诉我过程吗?](/uploads/image/z/3740413-13-3.jpg?t=sin%26%23178%3B20%C2%B0%EF%BC%8Bcos%26%23178%3B50%C2%B0%EF%BC%8Bsin20%C2%B0cos50%C2%B0%EF%BC%9D%EF%BC%BF%EF%BC%BF%3F+%E8%83%BD%E5%91%8A%E8%AF%89%E6%88%91%E8%BF%87%E7%A8%8B%E5%90%97%3F)
sin²20°+cos²50°+sin20°cos50°=__? 能告诉我过程吗?
sin²20°+cos²50°+sin20°cos50°=__? 能告诉我过程吗?
sin²20°+cos²50°+sin20°cos50°=__? 能告诉我过程吗?
sin²20°+cos²50°+sin20°cos50°
=(1-cos40°)/2+(1+cos100°)/2+(1/2)*(sin70°-sin30°)
=(1-cos40°)/2+(1-cos80°)/2+(1/2)*(cos20°-1/2)
=1-(1/2)*(cos40°+cos80°)+(1/2)*(cos20°-1/2)
=1-(cos60°cos20°)+(1/2)cos20°-1/4
=1-(1/2)cos20°+(1/2)cos20°-1/4
=3/4;
sin²20°+cos²50°+sin20°cos50°
=(sin20°+cos50°)^2-sin20°cos50°
=(sin20°+sin40°)^2-sin20°cos50°
=(2sin30cos10)^2-sin20°cos50°
=(cos10°)^2--[sin70-sin30]/2
=(1+cos20°)/2 -[cos20°-1/2]/2
=3/4;
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