若sinx-2cosy=根号2cosx+2sinx=2则sin(x-y) 已知sinx+siny=根号2/2,则cosx+cosy的取...
\u82e5sinx-2cosy=2\uff0ccosx+2siny=2\uff0c\u5219sin\uff08x-y\uff09=?14?14\u7531sinx-2cosy=2\uff0ccosx+2siny=2\uff0c\u5f97\uff08sinx-2cosy\uff092=2\uff0c\uff08cosx+2siny\uff092=4\uff0c\u5373sin2x-4sinxcosy+4cos2y=2\u4e14cos2x+4cosxsiny+4sin2y=4\uff0c\u4e24\u5f0f\u76f8\u52a0\u5f971+4sin\uff08y-x\uff09+4=2+4=6\uff0c\u5373sin\uff08x-y\uff09=-14\uff0c\u6545\u7b54\u6848\u4e3a\uff1a?14\uff1b
\u56e0\u4e3acos(x-y)\u7684\u503c\u57df\u662f\u3010-1,1\u3011\uff0c\u6240\u4ee5-1\u2264(2t^2-3)/4\u22641 \u3002
2cosx^2+4sinx^2+16sinxcosx=4=>2sinx^2+16sinxcosx=2
=>1-cos2x+8sin2x=2
=>8sin2x-cos2x=1 (1)
sin2x^2+cos2x^2 = 1 (2)
(1)和(2)=>sin2x=0或者sin2x=16/65
当sin2x=0时 cos2x = -1 =>2x = (2k+1)pai=>x=(k+1/2)pai
sinx = 1 cosx=0
或者sinx=-1 cosx=0 (sinx-2cosy=2不可能满足)
sinx=1 cosy= -1/2=>siny = (3/4)^(1/2)
sin(x-y) = sinxcosy-sinycosx=sinxcosy=1*(-1/2) = -1/2
当sin2x=16/65时,cos2x=63/65=>1-sinx^2=cos2x=63/65=>sinx^2 = 2/65=>sinx=(2/65)^(1/2)
由根号2cosx+2sinx=2=>sinx>=0 cosx>=0
cosx = (63/65)^(1/2)
2cosy= 2-(2/65)^(1/2) siny可求
再代入原式，可求结果
绛旓細=2(1-cos2x)/2+sin2x =sin2x-cos2x+1 鏍规嵁杈呭姪瑙掑叕寮 =鏍瑰彿2*sin(2x-娲/4)+1 鎵浠ユ渶澶у间负 鏍瑰彿2+1 绗簩棰 sinz=sinx-siny 锛1锛塩osz=cosy-cosx 锛2锛夛紙1锛塣2+锛2锛塣2,寰 1=(sinx)^2+(siny)^2-2sinxsiny+(cosy)^2+(cosx)^2-2cosxcosy sinxsiny+cosxcosy=1/2 cos(...
绛旓細杩欎釜鏄鏈笂鐨勫叕寮忥紝浣犲彲浠ョ櫨搴︿竴涓嬶紝鎶婂叕寮忚涓嬫潵 姣斿asinx+bcosy鍙互鍖栦负;鏍瑰彿(a^2+b^2)sin(x+w)鍏朵腑:cosw=a/鏍瑰彿(a^2+b^2)sinw=b/鏍瑰彿(a^2+b^2)tanw=sinw/cosw=b/a
绛旓細杈呭姪瑙掑叕寮 y=sinx+cosx =鏍瑰彿2sin锛坸+蟺/4)0鈮鈮2蟺 蟺/4鈮鈮9/4蟺 鎵浠 -1鈮in锛坸+蟺/4)鈮1 -鏍瑰彿2鈮ゆ牴鍙2sin锛坸+蟺/4))鈮ゆ牴鍙2 鎵浠in=-鏍瑰彿2 max=鏍瑰彿2
绛旓細鍜屽樊鍖栫Н鍏紡锛歴inx+siny=2sin[(x+y)/2]cos[(x-y)/2]鈭磗inx+cosy =sinx+sin(蟺/2-y)=2sin[(x-y+蟺/2)/2]cos[(x+y-蟺/2)/2]=2sin[(x-y)/2+蟺/4]cos[(x+y)/2-蟺/4]
绛旓細y=sinx+2cosx=鏍瑰彿5锛1/鏍瑰彿5*sinx+2/鏍瑰彿5*cosx锛 浠1/鏍瑰彿5=cosy 2/鏍瑰彿5=siny 鎵浠=鏍瑰彿5*sin锛坸+y锛夋渶澶у间负鏍瑰彿5锛屾渶灏忓间负-鏍瑰彿5
绛旓細浣犻偅涓眰cos x=cos y 锛燂紵锛燂紝鏄姞杩樻槸鍑忥紝鎶婁笂闈㈤厤鏂逛竴涓嬶紝鎴戞寜鍔犵畻浜嗭紝寰楋紙cosx+cosy锛夋柟=2sinxsiny+2cosxcosy锛岀劧鍚庣敤绉寲鍜屽樊鍏紡鍖栫畝寰楋紙cosx+cosy锛夋柟=2cos(x-y)銆傜敱浜巗inx+siny=鏍2锛屽苟涓攕iny<=1锛屾晠sinx>=鏍2-1.鍚岀悊siny>=鏍2-1锛屽彲寰楋紙x-y锛夊睘浜(m掳锛90掳锛夛紝cos锛坸-...
绛旓細鑻=135掳,y=45掳,鍒檆osx-siny=-鈭2.鎵浠ヨ繖涓瓟妗堟槸閿欒鐨勩傞偅涔堬紝cosx-siny鐨勫彇鍊艰寖鍥寸┒绔熸槸澶氬皯鍛紵鍓嶉潰鎴戞彁鍒颁簡鈥濅笁瑙掑嚱鏁板叿鏈夋湁鐣屾р滐紝鐨勭‘锛屽彲浠ュ埄鐢ㄤ笁瑙掑嚱鏁扮殑鏈夌晫鎬ф潵瑙ｅ喅杩欎釜闂銆備负浜嗕娇闂绠鍖栵紝鎴戜滑鍙互浠=x,Y=-y,閭ｄ箞鏈灏卞彉涓 "宸茬煡sinXcosY=1/2,鍒檆osX+sinY鐨勫彇鍊艰寖鍥存槸锛"...
绛旓細cosx-cosy=2/3 鈥︹︹憽 鈶燸2 : (sinx)^2-2sinxsiny+(siny)^2=4/9 鈥︹︹憿 鈶2 : (cosx)^2-2cosxcosy+(cosy)^2=4/9 鈥︹︹懀 鈶+鈶ｏ細2-2锛坈osxcosy+sinxsiny)=8/9 鍗 2-2cos(x-y)=8/9 鈭碿os(x-y)=5/9 鈭祍inx-siny<0 鍗硈inx<siny 鈭磝<y鍗硏-y鏄礋閿愯...
绛旓細(1)y=sinxcosx=0.5sin2x,鎵浠ュ叾鍛ㄦ湡涓篜I 鍊煎煙涓猴紙-0.5,0.5锛.y=cosx+sinx=2^0.5*sin(x+pi/2),鎵浠ュ叾鍛ㄥ叾涓2PI,鍊煎煙涓猴紙-2^0.5,2^0.5锛夊洜鑰屽浜庢牴鎹笅3鐨刌,鍏跺懆鏈熸槸涓嶅彉鐨,鍊煎煙鍙鎶婂師鏉ョ殑寮涓夋鏂瑰氨鍙互浜.
绛旓細褰揧鍙栧緱鏈澶у兼椂锛宼anx=1/2
