设sin(x+y)=a,sin(x-y)=b,则sinxcosy等于？ 求证sin(x+y)=sinxcosy+cosxsiny 我...
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sin(x+y)=asinxcosy+sinycosx=a
sin(x-y)=b
sinxcosy-sinycosx=b
两式相加
2sinxcosy=a+b
sinxcosy=（a+b）/2
sin(x+y)=sinxcosy+sinycosx
sin(x-y)=sinxcosy-sinycosx
把上边两个式子相加得
sin(x+y)+sin（x-y)=2sinxcosy
a+b=2sinxcosy
sinxcosy=(a+b)/2
解：sin(x+y)+sin(x-y)=sinxcony+cosxsiny+sinxcosy-cosxsiny=2sinxcosy=a+b
sinxcosy=(a+b)/2
绛旓細sin(x-y)=b sinxcosy-sinycosx=b 涓ゅ紡鐩稿姞 2sinxcosy=a+b sinxcosy=锛坅+b锛/2
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