已知sin(x-y)cosx-cos(x-y)sinx=4/5且y是第三象限角，则cosy/2的值
\u5df2\u77e5cos(x-y)cosx+sin(x-y)sinx=3/5,\u5219cosy\u7684\u503c\u4e3acos(x-y)cosx+sin(x-y)sinx\uff1dcos\uff08x-y-x\uff09=cos(-y)=cosy=3/5
\u89e3\uff1a
sinx+siny=1/3,cosx-cosy=1/5
\u4e24\u5f0f\u5206\u522b\u5e73\u65b9\u5f97
sin²x+sin²y+2sinxsiny=1/9
cos²x+cos²y-2cosxcosy=1/25
\u76f8\u52a0\u5f97
1+1+2sinxsiny-2cosxcosy=1/9+1/25=34/225
2cosxcosy-2sinxsiny=2-34/225
cosxcosy-sinxsiny=1-17/225=208/225
\u2234cos(x+y)=208/225
绛旓細sin(x-y)cosx-cos(x-y)sinx=sin[(x-y)-x]=sin(-y)=-siny=3/5siny=-3/5sin²y+cos²y=1鎵浠os²y=16/25cosy=4/5鎴-4/5tany=siny/cosy=-3/4鎴3/4tan2y=2tany/(1-tan²y)=卤(3/2)/(1-9/16)=卤8/3 ...
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绛旓細鍙互鍖栦负(sinxcosy-cosxsiny)cosx-(cosxcosy+sinxsiny)sinx=3 sinxcosxcosy-cos²xsiny-sinxcosxcosy-sin²xsiny=3 -siny(cos²x+sin²x)=3 siny=-3 鐢辨寮﹀嚱鏁扮殑鍊煎煙鍙煡锛屾柟绋嬫棤瑙
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绛旓細-siny+sin(x-y)=0 鐩稿姞寰 cosx=siny sinx=cosy鎴杝inx=-cosy 1.褰搒inx=cosy鏃 鍙坈osx-sin(x-y)=cosx-sinxcosy+cosxsiny=0 鈭磗iny-cos²y+sin²y=0 2sin²y+siny-1=0 锛坰iny+1锛夛紙2siny-1锛=0 siny=-1锛屾垨siny=1/2 cosx=-1鎴栤垰3/2 x>=0 y<=90搴 鈭磝=...
绛旓細搴旇鏄Sin(x+y)Cosx-Cos(x+y)Sinx=3/5 sin[(x+y)-x]=3/5 siny=3/5 sin²y+cos²y=1 鎵浠osy=卤4/5 tany=siny/cosy=卤3/4 tan2y=2tany/(1-tan²y)=(卤3/2)/(7/16)鎵浠an2y=-24/7鎴24/7
绛旓細宸茬煡x锛寉涓洪攼瑙掞紝涓旀弧瓒砪os x= 锛sinx= 锛沜os锛坸+y锛= 锛sin锛坸+y锛= sin y=sim锛坸+y-x锛=sin锛坸+y锛塩osx-cos锛坸+y锛塻inx= 鏁呴塁
绛旓細sin锛坸+y锛塩osy-cos锛坸+y锛塻iny=0,鍥犱负sin锛坸+y锛塩osy-cos锛坸+y锛塻iny =sin[(x+y)-y]=sinx 鎵浠inx=0 閭ｄ箞sin锛坸+2y锛+sin锛坸-2y锛=sinxcos2y+cosxsin2y+sin2xcos2y-cosxsin2y =2sinxcos2y =2*0*cos2y =0
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绛旓細sin(x-y)=cos[蟺/2-(x-y)]=cos[(蟺/2+y)-x]=cos(蟺/2+y)cosx+sin(蟺/2+y)sinx =-siny*cosx+cosy*sinx =sinxcosy-cosxsiny tan(x-y)=sin(x-y)/cos(x-y)=(sinxcosy-cosxsiny/(cosxcosy+sinxsiny) 鍒嗗瓙鍒嗘瘝鍚岄櫎cosxcosy =(tanx-tany)/(1+tanxtany)...
