cosx)^2/[cosxsinx-(sinx)^2]化简
\u5316\u7b80:(1+cosx-sinx)/(1-cosx-sinx)+(1-cosx-sinx)/(1+cosx-sinx)(1+cosx-sinx)/(1-cosx-sinx)+(1-cosx-sinx)/(1+cosx-sinx)
=[(1+cosx-sinx)(1+cosx+sinx)]/[(1-cosx-sinx)(1+cosx+sinx)]
+[(1-cosx-sinx)(1-cosx+sinx)]/[(1+cosx-sinx)(1-cosx+sinx)]
=(1+2cosx+cos2x)/(-sin2x)+(1-2cosx+cos2x)/(sin2x)
=(-4cosx)/sin2x
=-2/sinx
y=\u221a2*cos(x-45\u00b0\uff09+(1/2)*sin(2x)
分子分母同时乘以一个cos平方x，得到1/tanx-tan平方x.绛旓細cosx^2绛変簬1-(sinx)^2銆俿ecx=1/cosx锛宻ec²x=1+tan²x锛宻ecxcosx=1锛宼anx=sinxsecx銆傛鍓诧紙sec锛夋槸涓夎鍑芥暟鐨勪竴绉嶃傚畠鐨勫畾涔夊煙涓嶆槸鏁翠釜瀹炴暟闆嗭紝鍊煎煙鏄粷瀵瑰煎ぇ浜庣瓑浜庝竴鐨勫疄鏁般傚畠鏄懆鏈熷嚱鏁帮紝鍏舵渶灏忔鍛ㄦ湡涓2蟺銆備綑寮﹀畾鐞嗭紝娆ф皬骞抽潰鍑犱綍瀛﹀熀鏈畾鐞嗐備綑寮﹀畾鐞嗘槸鎻忚堪涓夎褰腑涓夎竟闀垮害涓...
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細鑻ユ湁甯姪锛岃閲囩撼銆
绛旓細y'=2cosx.(cosx)'=2cosx(-sinx)=-sin2x
绛旓細(cosx)^2鐨勭瓑浠锋棤绌峰皬 鎴戞潵绛 鍒嗕韩 寰俊鎵竴鎵 缃戠粶绻佸繖璇风◢鍚庨噸璇 鏂版氮寰崥 QQ绌洪棿 涓炬姤 娴忚5 娆 鍙変腑1涓垨澶氫釜涓嬮潰鐨勫叧閿瘝,鎼滅储鐩稿叧璧勬枡銆備篃鍙洿鎺ョ偣鈥滄悳绱㈣祫鏂欌濇悳绱㈡暣涓棶棰樸 绛変环鏃犵┓灏 cosx 鎼滅储璧勬枡 鏈湴鍥剧墖 鍥剧墖閾炬帴 鎻愪氦鍥炵瓟 鍖垮悕 鍥炵瓟鑷姩淇濆瓨涓 浣犵殑鍥炵瓟琚噰绾冲悗灏嗚幏寰: 绯荤粺濂栧姳...
绛旓細(1/2)x+(1/4)sin2x+c銆傗埆cos²xdx =(1/2)鈭(1+cos2x)dx =(1/2)x+(1/4)sin2x+c 姹備笉瀹氱Н鍒嗙殑鏂规硶锛氱涓绫绘崲鍏冨叾瀹炲氨鏄竴绉嶆嫾鍑戯紝鍒╃敤f'(x)dx=df(x)锛涜屽墠闈㈢殑鍓╀笅鐨勬濂芥槸鍏充簬f锛坸锛夌殑鍑芥暟锛屽啀鎶奻锛坸锛夌湅涓轰竴涓暣浣擄紝姹傚嚭鏈缁堢殑缁撴灉銆傦紙鐢ㄦ崲鍏冩硶璇达紝灏辨槸鎶奻锛坸...
绛旓細浠^2=t鍒檟=sqrt(t)鍗砫x=dt/(2sqrt(t))鍝箞鈭玞os(x^2)dx=鈭玞os(t)[1/(2sqrt(t))]dt 鍐嶇敤鍒嗛儴绉垎娉曞幓绉 鐢ㄦ嘲鍕掑睍寮寮 cosx=1-x^2/2!+x^4/4!+鈥+(-1)^m脳x^(2m)/(2m)!+鈥﹂偅涔坈os(x^2)=1-x^4/2!+x^8/4!+鈥+(-1)^m脳x^(4m)/(2m)!+鈥﹂偅涔 鈭玞os(x...
绛旓細(cosX)²=(1+cos2X)/2,瀵煎嚱鏁颁负-sin2X
绛旓細寰堢畝鍗曪紝鍥犱负锛cosx锛塣2鏄鍚堝嚱鏁帮紝澶嶅悎鍑芥暟姹傚鍜屾眰绉兘蹇呴』娉ㄦ剰锛屾眰绉殑鏃跺欏繀椤诲寲鎴愮畝鍗曞嚱鏁版墠鍙.濡傛灉鐩存帴绛変簬(sinx)^2锛屼綘鑷繁妫楠屼竴涓嬶紝(sinx)^2姹傚鍚庢槸鍚︾瓑浜庯紙cosx)^2锛屾樉鐒朵笉鐩哥瓑锛屾墍浠(sinx)^2涓嶆槸锛坈osx)^2鐨勫師鍑芥暟
绛旓細cosx^2鐨勪笉瀹氱Н鍒 =1/2鈭(1+cos2x)dx =1/2鈭1dx+1/2鈭玞os2xdx =1/2x+1/4鈭玞os2xdx =1/2x+1/4sin2x+C
绛旓細cosx^2鐨勫鏁版槸-2xsin(x^2)姹傚杩囩▼锛歽=cos(x^2)鍒檡'=-sin(x^2)*(x^2)'=-2xsin(x^2)濡傛灉鏄痽=cos(x^2)鍒檡'=-sin(x^2)*(x^2)'=-2xsin(x^2)姹傚鏁帮細瀵逛簬鍙鐨勫嚱鏁癴(x)锛寈↦f'(x)涔熸槸涓涓嚱鏁帮紝绉颁綔f(x)鐨勫鍑芥暟锛堢畝绉板鏁帮級銆傚鎵惧凡鐭ョ殑鍑芥暟鍦ㄦ煇鐐圭殑瀵兼暟鎴...
