根号2（sinx－cosx）化简 cosx-sinx怎么化简？ sinx-cosx怎么化简？

sinx(sinx-cosx)\u7684\u5316\u7b80

=sin\u5e73\u65b9x-sinxcosx
=1/2(2sin\u5e73\u65b9x-2sinxcosx)
=1/2(1-cos2x-sin2x)
=1/2-\u68392/2sin(2x+45\u5ea6)

\u89e3\u9898\u6b65\u9aa4\u5982\u4e0b
cosx-sinx
=\u221a(cosxcos45\u00b0-sinxsin45\u00b0)
=\u221acos(x+45\u00b0)
sinx-cosx
=\u221a(sinxcos45\u00b0-cosxsin45\u00b0)
=\u221asin(x-45\u00b0)

\u6269\u5c55\u8d44\u6599
\u4e09\u89d2\u51fd\u6570\u662f\u57fa\u672c\u521d\u7b49\u51fd\u6570\u4e4b\u4e00\uff0c\u662f\u4ee5\u89d2\u5ea6\uff08\u6570\u5b66\u4e0a\u6700\u5e38\u7528\u5f27\u5ea6\u5236\uff0c\u4e0b\u540c\uff09\u4e3a\u81ea\u53d8\u91cf\uff0c\u89d2\u5ea6\u5bf9\u5e94\u4efb\u610f\u89d2\u7ec8\u8fb9\u4e0e\u5355\u4f4d\u5706\u4ea4\u70b9\u5750\u6807\u6216\u5176\u6bd4\u503c\u4e3a\u56e0\u53d8\u91cf\u7684\u51fd\u6570\u3002
\u5e38\u89c1\u7684\u4e09\u89d2\u51fd\u6570\u5305\u62ec\u6b63\u5f26\u51fd\u6570\u3001\u4f59\u5f26\u51fd\u6570\u548c\u6b63\u5207\u51fd\u6570\u3002\u5728\u822a\u6d77\u5b66\u3001\u6d4b\u7ed8\u5b66\u3001\u5de5\u7a0b\u5b66\u7b49\u5176\u4ed6\u5b66\u79d1\u4e2d\uff0c\u8fd8\u4f1a\u7528\u5230\u5982\u4f59\u5207\u51fd\u6570\u3001\u6b63\u5272\u51fd\u6570\u3001\u4f59\u5272\u51fd\u6570\u3001\u6b63\u77e2\u51fd\u6570\u3001\u4f59\u77e2\u51fd\u6570\u3001\u534a\u6b63\u77e2\u51fd\u6570\u3001\u534a\u4f59\u77e2\u51fd\u6570\u7b49\u5176\u4ed6\u7684\u4e09\u89d2\u51fd\u6570\u3002\u4e0d\u540c\u7684\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u4ee5\u901a\u8fc7\u51e0\u4f55\u76f4\u89c2\u6216\u8005\u8ba1\u7b97\u5f97\u51fa\uff0c\u79f0\u4e3a\u4e09\u89d2\u6052\u7b49\u5f0f
\u53c2\u8003\u8d44\u6599\u6765\u6e90
\u767e\u5ea6\u767e\u79d1-\u4e09\u89d2\u51fd\u6570\u516c\u5f0f

解：
√2（sinx-cosx）

=2(sinx*√2/2-√2/2*cosx)

=2(sinx*cos45º-sin45º*cosx)

=2sin(x-45º)

图片格式为

楼上正解

鏍瑰彿2(sinx-cosx) 鎬庝箞鍖栫畝? (璇︾粏杩囩▼)
绛旓細鈭2锛坰inx-cosx锛=2脳鈭2/2锛坰inx-cosx锛=2锛坰inx鈭2/2-cosx鈭2/2锛=2锛坰inxcox45-cosxsin45锛=2锛坰inx-45锛夋敞鏄庯細鈭氳繖涓槸鏍瑰彿锛岄偅涓45鏄寚45搴︺

鍖栫畝鏍瑰彿2(sinx-cosx)
绛旓細鏍瑰彿2(sinx-cosx)=2(鈭2/2sinx-鈭2/2cosx锛=2(sinxcos蟺/4-cosxsin蟺/4)=2sin(x-蟺/4)

鏍瑰彿2(sinx-cosx)鍖栫畝
绛旓細瑙ｏ細鈭2锛坰inx-cosx锛=2(sinx*鈭2/2-鈭2/2*cosx)=2(sinx*cos45º-sin45º*cosx)=2sin(x-45º)鍥剧墖鏍煎紡涓

鏍瑰彿2(sinx-cosx) 瑕佹眰鏄埄鐢ㄥ拰宸叕寮忓寲绠 鏈夋ョ敤,鏄庡ぉ灏卞彨浣滀笟浜...
绛旓細鍘熷紡=2(sinx*鈭2/2-cosx*鈭2/2)=2(sinxcos蟺/4-cosxsin蟺/4)=2sin(x-蟺/4)

鏍瑰彿浜涔樹互(sinx-cosx)鍖栨垚鍟sin(x+灞)鐨勫舰寮
绛旓細鈭2(sinx-cosx)=2cos45掳sinx-2sin45掳cosx=2sin(x-45掳)濡傛灉璇ラ棶棰樿В鍐充簡,璇疯寰楃粰濂借瘎鎴栫偣閲囩撼鍝 ^

宸茬煡:鍑芥暟f(x)=鈭2(sinx-cosx)
绛旓細f(x)=鈭2(sinx-cosx)=2sin锛坸-蟺/4锕歠(x)鐨勬渶灏忔鍛ㄦ湡2蟺 鍊煎煙[锕2,2]2sin锛埼-蟺/4锕=6/5 sin锛埼-蟺/4锕=3/5,伪-蟺/4鈭堬箼0,蟺/2锕歝os锛埼-蟺/4锕=4/5 f(蟺/4+伪)=2sin伪=2sin[锛埼-蟺/4锕+蟺/4]=2锕3/5脳鈭2锛2+4/5脳鈭2锛2锕=7鈭2锛5 ...

宸茬煡;鍑芥暟f(x)=鏍瑰彿2(sinx-cosx),姹傚嚱鏁癴(x)鐨勬渶灏忔鍛ㄦ湡鍜屽..._鐧惧害...
绛旓細绗竴姝ワ細鏄彁璧峰叕鍥犲紡鈭2,涓庡闈㈢殑鈭2鐩镐箻灏卞緱鍒2!绗浜姝ワ細鎻愯捣鍏洜寮忊垰2鍚,鍘熸潵sinx涓cosx鍓嶉潰鐨勭郴鏁版槸1,鎻愯捣鍏洜寮忊垰2鍚庡垯鍙樹负鈭2/2,绗笁姝ワ細灏嗏垰2/2鎹㈡垚sin蟺/4鍜宑os蟺/4 鍥犱负sin蟺/4锛漜os蟺/4锛濃垰2/2 鏈鍚庡氨鏄叕寮忎簡!鑻ヨ繕涓嶆噦,

鍑芥暟f(x)=sinx-cosx 鍖栫畝?
绛旓細f(x)=sinx-cosx =(鏍瑰彿2)[(鏍瑰彿2/2)sinx-cosx(鏍瑰彿2/2)]=(鏍瑰彿2)[cos45sinx-cosxsin45]=(鏍瑰彿2)sin(x-45)

璇烽棶鎬庝箞鎵嶈兘鎶sinx-cosx鈮0 鍖栫畝鎴:鏍瑰彿2sin(x-蟺/4)鈮0
绛旓細鎻愪竴涓鏍瑰彿2鍑烘潵 鐒跺悗2鍒嗕箣鏍瑰彿2=sin45. 鍚庨潰鍙互鐢ㄥ叕寮忎簡锛

宸茬煡鍑芥暟f(x)=鏍瑰彿2(sinx-cosx),姹(1)鍑芥暟f(x)鐨勫煎煙(2)鑻ュ嚱鏁扮殑鍥捐薄...
绛旓細f(x)=2sin(x-45) 鍊煎煙涓篬-2,2]-鍏/2+2k鍏<=x-鍏/4<=鍏/2+2k鍏 -鍏/4+2k鍏<=x<=3鍏/4+2k鍏 6/5=2sin(a-鍏/4)sin(a-鍏/4)=3/5 鍏/4<a<3/4鍏 鍏/2<鍏/4+a<鍏 0<a-鍏/4<鍏/2鍦-鍏/4+2k鍏<=x<=3鍏/4+2k鍏鍐 f(鍏/4+a)=2sin(a+鍏/4-鍏/4...