证明sin(x+y)sin(x-y)=sinx-siny

学习 时间:2026-08-14 15:57:05 阅读:7003
证明sin(x+y)sin(x-y)=sinx-siny

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2026-08-14 15:57:05

sin(x+y)sin(x-y) =-1/2(cos(x+y+x-y)—cos(x+y-x+y)) =-1/2(cos2x—cos2y) =-1/2(1-2(sinx)^2-1+2(siny)^2) =(sinx)^2-(siny)^2

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    2026-08-14 15:57:05

    sin(x+y)sin(x-y) =-1/2(cos(x+y+x-y)—cos(x+y-x+y)) =-1/2(cos2x—cos2y) =-1/2(1-2(sinx)^2-1+2(siny)^2) =(sinx)^2-(siny)^2

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