cos²α+cos²(120°-α)+cosαcos(120°-α) cos²α+cos²(120°-α)+cosαcos(120°-α)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 13:17:43
![cos²α+cos²(120°-α)+cosαcos(120°-α) cos²α+cos²(120°-α)+cosαcos(120°-α)](/uploads/image/z/383782-22-2.jpg?t=cos%26%23178%3B%CE%B1%2Bcos%26%23178%3B%EF%BC%88120%C2%B0-%CE%B1%EF%BC%89%2Bcos%CE%B1cos%EF%BC%88120%C2%B0-%CE%B1%EF%BC%89+cos%26%23178%3B%CE%B1%2Bcos%26%23178%3B%EF%BC%88120%C2%B0-%CE%B1%EF%BC%89%2Bcos%CE%B1cos%EF%BC%88120%C2%B0-%CE%B1%EF%BC%89)
cos²α+cos²(120°-α)+cosαcos(120°-α) cos²α+cos²(120°-α)+cosαcos(120°-α)
cos²α+cos²(120°-α)+cosαcos(120°-α)
cos²α+cos²(120°-α)+cosαcos(120°-α)
cos²α+cos²(120°-α)+cosαcos(120°-α) cos²α+cos²(120°-α)+cosαcos(120°-α)
原式
=(cosα+cos(120°-α))²-cosαcos(120°-α)
=(2cos60°cos(α-60°))²-(cos120°+cos(2α-120°))/2 ----利用和差化积、积化和差公式,可以百科搜
=cos²(α-60°)-(cos(2α-120°))/2+1/4
=(1+cos(2α-120°))/2-cos(2α-120°))/2+1/4
=3/4