证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
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证明sin(a+b)sin(a-b)=sin^2a-sin^2b,证明sin(a+b)sin(a-b)=sin^2a-sin^2b,证明sin(a+b)sin(a-b)=sin^2a-sin^2b,左
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
证明sin(a+b)sin(a-b)=sin^2 a-sin^2 b,
左边=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin²acos²b-cos²asin²b
=sin²a(1-sin²b)-(1-sin²a)sin²b
=sin²a-sin²asin²b-sin²b+sin²asin²b
=sin²a-sin²b
=右边
命题得证
将左边的式子完全打开即可得到右边的式子。
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