1/2(cos2a-cos2b)=sin(a+b)sin(a-b)吗?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/23 06:09:36
1/2(cos2a-cos2b)=sin(a+b)sin(a-b)吗?
不等于sin(a+b)sin(a-b),应该等于-sin(a+b)sin(a-b)
(1/2)(cos2A-cos2B)
=(1/2){cos[(A+B)+(A-B)]-cos[(A+B)-(A-B)]}
=(1/2)[cos(A+B)cos(A-B)-Sin(A+B)sin(A-B)]
-(1/2)[cos(A+B)cos(A-B)+sin(A+B)sin(A-B)]
=(1/2)sin(A+B)sin(A-B)+(1/2)sin(A+B)sin(A-B)
=-sin(A+B)sin(A-B)
(1/2)(cos2A-cos2B)
=(1/2){cos[(A+B)+(A-B)]-cos[(A+B)-(A-B)]}
=(1/2)[cos(A+B)cos(A-B)-Sin(A+B)sin(A-B)]
-(1/2)[cos(A+B)cos(A-B)+sin(A+B)sin(A-B)]
=(1/2)sin(A+B)sin(A-B)+(1/2)sin(A+B)sin(A-B)
=-sin(A+B)sin(A-B)
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