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求证(sinx-siny)/sin(x+y)=sin1/2(x-y)/sin1/2(x+y)不要网上复制的,用半角公式
题目详情
求证(sinx-siny)/sin(x+y) = sin1/2(x-y)/sin1/2(x+y) 不要网上复制的,用半角公式
▼优质解答
答案和解析
(sinx-siny)/sin(x+y)
=[2sin(x/2)cos(x/2)-2sin(y/2)cos(y/2)]/2sin[(x+y)/2]cos[(x+y)/2]
=[sin(x/2)cos(x/2)-sin(y/2)cos(y/2)]/sin[(x+y)/2]cos[(x+y)/2]
=sin[1/2(x-y)]/sin[1/2(x+y)]
=[2sin(x/2)cos(x/2)-2sin(y/2)cos(y/2)]/2sin[(x+y)/2]cos[(x+y)/2]
=[sin(x/2)cos(x/2)-sin(y/2)cos(y/2)]/sin[(x+y)/2]cos[(x+y)/2]
=sin[1/2(x-y)]/sin[1/2(x+y)]
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