求证：sin(A+B)sin(A-B)=sinAsinA-sinBsinB

来源：百度知道编辑：UC知道时间：2024/05/10 08:33:35

求证啊·！急用~！

解：
令a=A，b=B
则
sin(A+B)sin(A-B)-(sinAsinA-sinBsinB)
=(sinacosb+cosasinb)(sinacosb-cosasinb)-(sinAsinA-sinBsinB)
=sin^2acos^2b-cos^2asin^2b-sin^2a+sin^2b

=sin^2a(cos^2b-1)-sin^2b(cos^2a-1)
=(cos^2a-1)sin^2b-sin^2b(cos^2a-1)
=0
所以命题得证
所以sin(A+B)sin(A-B)=sinAsinA-sinBsinB

不对的“公式”

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