作业帮sin(A-B)=0,求证cos(A-2B)=cosA
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 16:41:21
sin(A-B)=0,求证cos(A-2B)=cosA
sin(A-B)=0,求证cos(A-2B)=cosA
sin(A-B)=0,求证cos(A-2B)=cosA
cos(A-2B)=cos(2A-2B-A)=cos(2A-2B)cosA+sin(2A-2B)sinA=cos2(A-B)cosA+sin2(A-B)sinA
=cos2(A-B)cosA=[1-2sin(A-B)^2]cosA=cosA.
sin(A-B)=0，
A-B=kπ
B=A-kπ
2B=2A-2kπ
cos(A-2B)=cos(A-2A+2kπ)=cos(-A+2kπ)=cos(-A)=cosA
sin2(A-B)=2sin(A-B)cos(A-B)=0
cos2(A-B)=1-2sin²(A-B)=1
cos(A-2B)
=cos[2(A-B)-A]
=cos2(A-B)cosA+sin2(A-B)sinA
=1*cosA+0*sinA
=cosA
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