3sinx-cosx怎么化简 cosx-sinx怎么化简？ sinx-cosx怎么化简？

\u6839\u53f73sinx+cosx\u5982\u4f55\u5316\u7b80

\u89e3\u221a3sinx+cosx
=2\uff08\u221a3/2sinx+1/2cosx\uff09
=2\uff08cos\u03c0/6sinx+sin\u03c0/6cosx\uff09
=2sin\uff08x+\u03c0/6)

\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：原式=√3sinx-cosx
=2(sinxcosπ/6-cosxsinπ/6)
=2sin(x-π/6)

3sinx-cosx鎬庝箞鍖栫畝
绛旓細瑙ｏ細鍘熷紡=鈭3sinx-cosx =2(sinxcos蟺/6-cosxsin蟺/6)=2sin(x-蟺/6)

sin3xcosx鎬庝箞鍖栫畝姹傚
绛旓細瑙ｏ細1銆乻in3x=sin(x+2x)=sinxcos2x+cosxsin2x =sinx*((cosx)^2-(sinx)^2)+cosx*2sinxcosx =sinx(cosx)^2-(sinx)^3+2sinx(cosx)^2 =3sinx(cosx)^2-(sinx)^3 2銆乧os3x=cos(x+2x)=cosxcos2x-sinxsin2x =cosx*((cosx)^2-(sinx)^2)-2(sinx)^2cosx =(cosx)^3-3(sinx)...

宸茬煡鍑芥暟f(x)=鈭3sinx-cosx,鍒欒鍑芥暟鍗曡皟閫掑噺鍖洪棿鏄,涓嶈杩囩▼,鍙绛旀...
绛旓細鍑芥暟鍙互鍖栫畝涓 f(x)=2锛堚垰3/2sinx-1/2cosx)=2(sin(x-蟺/6))鎵浠ラ掑噺鍖洪棿鏄 锛2K蟺+2/3蟺, 2K蟺+5/3蟺锛塊鏄釜鏁存暟,蟺鏄渾鍛ㄧ巼=3.1415926

sinx-cosx鐨鍘熷嚱鏁版槸浠涔
绛旓細杩欐槸涓涓亽绛夊紡锛屽搴旈」绯绘暟搴旇鐩哥瓑锛屾晠鏈夛細a-2b=1...鈶狅紱 2a+b=-1...鈶; 鈶犫憽鑱旂珛瑙ｅ緱a=-1/5锛宐=-3/5锛涙晠sinx-cosx=-(1/5)(sinx+2cosx)-(3/5)(sinx+2cosx)'锛涗唬鍏ュ師寮忓苟鍖栫畝寰楋細鈭玔(sinx-cosx)/(sinx+2cosx)]dx=-(1/5)鈭玠x-(3/5)鈭玔(sinx+2cosx)'/(sinx+...

cosx鐨勪笁娆℃柟鍑忓幓,sinx鐨勪笁娆℃柟绛変簬1,姹俋鐨勮В闆
绛旓細1-t^2)/2 =1 鍖栫畝寰楋紙t-1)*锛坱^2+t+2)=0 鎵浠=1 鎵浠cosx-sinx=2^锛1/2锛塩os(x+蟺/4)=1 鎵浠os(x+蟺/4)=2^(1/2)/2 寰梮+蟺/4=蟺/4+2k蟺 鎴杧+蟺/4=-蟺/4+2k蟺 鏁厁={2k蟺,-蟺/2+2k蟺} ^琛ㄧず骞傛柟 *琛ㄧず鐩镐箻 2^锛1/2锛夎〃绀烘牴鍙2 涓哄暐娌℃偓璧忓垎鐨?

3sinx-2cosx鐨勫寲绠
绛旓細杩囩▼濡傚浘锛

鈭3sinx+cosx鍖栫畝 鎷滄墭!涓囧垎鎰熻阿!
绛旓細璇烽噰绾

sin^3x-cos^3x鍖栫畝绛変簬澶氬皯
绛旓細瑙ｏ細sin³x-cos³x =(sinx-cosx)(sin²x+sinxcosx+cos²x)=(sinx-cosx)(1+sinxcosx)=sinx+sin²xcosx-cosx-sinxcos²x =sinx-cosx+½sinxsin2x-½cosxsin2x =sinx-cosx-¼(cos3x-cosx)-¼(sin3x+sinx)=-¼(sin3x+cos3x...

鏍瑰彿(3sinx+cosx)鎬庝箞鍖栫畝?
绛旓細鏍瑰彿锛3sinx+cosx锛=鏍瑰彿[鏍瑰彿锛3^2+1^2锛夛紙3/(鏍瑰彿3^2+1^2)锛塻inx+1/(鏍瑰彿3^2+1^2)cosx]=鏍瑰彿[鏍瑰彿10锛堬紙3/鏍瑰彿10锛塻inx+1/鏍瑰彿10cosx锛塢浠3/鏍瑰彿10=cos伪锛1/鏍瑰彿10=sin伪 鍒檛an伪=1/3 鍘熷紡=鏍瑰彿锛堟牴鍙10sin(x+伪)锛=10鏍瑰彿锛坰in锛坸+伪锛

cos3x鐨勫寲绠
绛旓細鍥炵瓟濡備笅锛歝os3x =cos(2x+x)=cos2xcosx-sin2xsinx =(2cos²x-1)cosx-2(1-cos²x)cosx =4cos³x-3cosx

扩展阅读：3sinx-4cosx ... sinx-xcosx怎么化解 ... 1-cosx sinx ... cos sin tan 基本公式 ... 根号3sinx cosx ... cossinx-cosx三角公式 ... asinx十bcosx万能公式 ... sinx除以1-cosx ... 辅助角公式化简sinx-cosx ...