若α+β=120°,则y=sin²α+cos²β的最小值是多少sin²α+cos²β=1-cos2α/2+1+cos2β/2=1+1/2(cos2β-cos2α)=1-sin(α+β)sin(β-α),1-sin(α+β)sin(β-α)这个怎么得来的
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/27 13:00:27
![若α+β=120°,则y=sin²α+cos²β的最小值是多少sin²α+cos²β=1-cos2α/2+1+cos2β/2=1+1/2(cos2β-cos2α)=1-sin(α+β)sin(β-α),1-sin(α+β)sin(β-α)这个怎么得来的](/uploads/image/z/666020-20-0.jpg?t=%E8%8B%A5%CE%B1%2B%CE%B2%3D120%C2%B0%2C%E5%88%99y%3Dsin%26%23178%3B%CE%B1%2Bcos%26%23178%3B%CE%B2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91sin%26%23178%3B%CE%B1%2Bcos%26%23178%3B%CE%B2%3D1-cos2%CE%B1%2F2%2B1%2Bcos2%CE%B2%2F2%3D1%2B1%2F2%EF%BC%88cos2%CE%B2-cos2%CE%B1%EF%BC%89%3D1-sin%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89sin%EF%BC%88%CE%B2-%CE%B1%EF%BC%89%2C1-sin%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89sin%EF%BC%88%CE%B2-%CE%B1%EF%BC%89%E8%BF%99%E4%B8%AA%E6%80%8E%E4%B9%88%E5%BE%97%E6%9D%A5%E7%9A%84)
若α+β=120°,则y=sin²α+cos²β的最小值是多少sin²α+cos²β=1-cos2α/2+1+cos2β/2=1+1/2(cos2β-cos2α)=1-sin(α+β)sin(β-α),1-sin(α+β)sin(β-α)这个怎么得来的
若α+β=120°,则y=sin²α+cos²β的最小值是多少
sin²α+cos²β=1-cos2α/2+1+cos2β/2=1+1/2(cos2β-cos2α)=1-sin(α+β)sin(β-α),
1-sin(α+β)sin(β-α)这个怎么得来的
若α+β=120°,则y=sin²α+cos²β的最小值是多少sin²α+cos²β=1-cos2α/2+1+cos2β/2=1+1/2(cos2β-cos2α)=1-sin(α+β)sin(β-α),1-sin(α+β)sin(β-α)这个怎么得来的
sin²α+cos²β
=(1-cos2α)/2+(1+cos2β)/2-----------公式:cos2a=cos²a-sin²a=2cos²a-1=1-2sin²a
=1+1/2(cos2β-cos2α)
=1-sin(α+β)sin(β-α)------------------公式:cosa-cosb=2sin(a-b)/2sin(a+b)/2