化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 19:35:48
![化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2](/uploads/image/z/6861727-55-7.jpg?t=%E5%8C%96%E7%AE%80%EF%BC%9A%28cosA%29%5E2%2B%5Bcos%282%2F3pai%2BA%29%5D%5E2%2B%5Bcos%282%2F3pai-A%29%5D%5E2)
化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2
化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2
化简:(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2
(cosA)^2+[cos(2π/3+A)]^2+[cos(2π/3-A)]^2
=(cosA)^2+[1+cos(4π/3+2A)]/2+[1+cos(4π/3-2A)]/2
=(cosA)^2+1/2+1/2*cos(4π/3+2A)+1/2+1/2*cos(4π/3-2A)
=(cosA)^2+1/2*cos(4π/3+2A)+1/2*cos(4π/3-2A)+1
=(cosA)^2+1/2*cos(π+π/3+2A)+1/2*cos(π+π/3-2A)+1
=(cosA)^2-1/2*cos(π/3+2A)-1/2*cos(π/3-2A)+1
=(cosA)^2-1/2*(cosπ/3cos2A-sinπ/3sin2A)-1/2*(cosπ/3cos2A+sinπ/3sin2A)+1
=(cosA)^2-1/2*[(cosπ/3cos2A-sinπ/3sin2A)+(cosπ/3cos2A+sinπ/3sin2A)]+1
=(cosA)^2-1/2*(cosπ/3cos2A-sinπ/3sin2A+cosπ/3cos2A+sinπ/3sin2A)+1
=(cosA)^2-cosπ/3cos2A+1
=(cosA)^2-1/2*cos2A+1
=(1+cos2A)/2-1/2*cos2A+1
=1/2+1/2*cos2A-1/2*cos2A+1
=1/2+1
=3/2
(cosA)^2+[cos(2/3pai+A)]^2+[cos(2/3pai-A)]^2
=(1+cos2A)/2 +[1+cos(4π/3+2A)]/2+ [1+cos(4π/3-2A)]/2
=3/2+1/2[cos2A+cos(4π/3+2A)+ cos(4π/3-2A)]
=3/2+1/2[ cos2A+2cos4π/3cos2A ]
=3/2+1/2[ cos2A+2(-1/2)cos2A]
=3/2