为什么sin^2(x)=1-cos^2(x) 为什么sin^{x}=[(1-cos2x)/2]^2
sin^2(x)+cos^2(x)=sin^2(x)+cos^2(x)=1
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绛旓細鐜板湪鎴戜滑瑕佹眰杩欎釜鏋侀檺 lim(x鈫0) sin(x)/(x+3)鏍规嵁涓婅堪瀹氱悊 褰搙鈫0鏃 sin(x)锝瀤 (閲嶈鏋侀檺涓) x+3锝瀤+3 锛岄偅涔坙im(x鈫0) sin(x)/(x+3)=lim(x鈫0) x/(x+3)=1 閲嶈鐨勭瓑浠锋棤绌峰皬鏇挎崲 褰搙鈫0鏃讹紝sinx~x tanx~x arcsinx~x arctanx~x 1-cosx~(1/2)*锛坸^2锛夛紙a^x...
绛旓細鍏蜂綋鍥炵瓟濡備笅锛歺鐨勫钩鏂/鏍瑰彿涓媋骞虫柟-x骞虫柟鐨勪笉瀹氱Н鍒=d绉垎锛坸/a)^2/鏍瑰彿锛1-锛坸/a)^2)dx 璁緓/a=sint鍒檟=asint锛宒x=acostdt 鍘=绉垎(sint)^2/cost*acostdt =绉垎a(sint)^2dt =a绉垎(1-cos2t)/2dt=a(t/2+sin2t/4)=(a/2)arcsin(x/a)+x鏍瑰彿锛1-(x/a)^2)+c 瑙ｉ噴 ...
绛旓細x = sin胃锛宒x = cos胃 d胃鈭 鈭(1 - x²) dx = 鈭 鈭(1 - sin²胃)(cos胃 d胃) = 鈭 cos²胃 d胃= 鈭 (1 + cos2胃)/2 d胃 = 胃/2 + (sin2胃)/4 + C= (arcsinx)/2 + (sin胃cos胃)/2 + C= (arcsinx)/2 + (x鈭(1 - x²))...
绛旓細11銆乪xdx=ex+C鈭玜x 12銆佲埆axdx=+Clna鈭玸in2xdx=鈭2sinxcosxdx=鈭2cosxsinxdx_=2鈭玞osx(_1)d(cosx)=_2鈭玞osxd(cosx)浠=cosx=_2鈭玼duu=_22+C=_u+C=_cosx+C_2鈭1_x2d(1_x2)1浠=1_x2_鈭玼du=23122=_23u+C3312122=_3u+C=_3(1_x)+C12d(1_x)_2 姹傚鍏紡 (x...
绛旓細cos(a+b)=cosacosb-sinasinb 浠=a 鍒 cos(2a)=cos²a-sin²a=(1-sin²a)-sin²a =cos²a-(1-cos²a)=1-2sin²a =2cos²a-1 涓よ鍜岋紙宸級鍏紡鍖呮嫭涓よ鍜屽樊鐨勬寮﹀叕寮忋佷袱瑙掑拰宸殑浣欏鸡鍏紡銆佷袱瑙掑拰宸殑姝ｅ垏鍏紡銆備袱瑙掑拰涓庡樊鐨勫叕寮忔槸...
绛旓細瀵逛簬B锛岀敤鍗婅鍏紡锛1-cosx=2(sin x/2)^2. 褰 x->0 鏃讹紝sin x/2~x/2锛屾墍浠 1-cosx=2(sin x/2)^2 鏄 x^2 鐨勫悓闃舵棤绌峰皬锛涘浜嶥锛屽綋 x->0 鏃讹紝鍒╃敤 ln(1+x)~x锛屽皢杩欓噷鐨剎鐢 x^2 浠ｆ崲锛屽氨鐭ラ亾 ln(1+x^2)~x^2锛屽畠浠篃鏄悓闃舵棤绌峰皬锛涚瓟妗堟槸C. 濡傛灉浣犲浜員aylor...
绛旓細瑙ｏ細鈭垰(1-x^2)dx 浠x=sint锛岄偅涔 鈭垰(1-x^2)dx=鈭垰(1-(sint)^2)dsint =鈭玞ost*costdt =1/2*鈭(1+cos2t)dt =1/2*鈭1dt+1/2*鈭玞os2tdt =t/2+1/4*sin2t+C 鍙坰int=x锛岄偅涔坱=arcsinx锛宻in2t=2sintcost=2x*鈭(1-x^2)鎵浠モ埆鈭(1-x^2)dx=t/2+1/4*sin2...
绛旓細e^x(1+e^x)^2] = 鈭玠u/[u(1+u)^2]= 鈭玔1/u-1/(1+u)-1/(1+u)^2]du = lnu-ln(1+u)+1/(1+u)+C = ln[e^x/(1+e^x)]+1/(1+e^x)+C;鈭(sinx)^2(cosx)^2dx = (1/4)鈭(sin2x)^2dx = (1/8)鈭(1-cos4x)dx = (1/8)[x-(1/4)sin4x]+C ...
绛旓細銆愮瓟妗堛戯細鍥爕=sin(x+C)锛寉'=cos(x+C)锛屾晠y'2+y2-1=cos2(x+C)+sin2(x+C)-1=0,鍗硑=sin(x+C)鏄師鏂圭▼鐨勮В锛屽張鍥犺В涓惈鏈変竴涓换鎰忓父鏁帮紝涓庢柟绋嬬殑闃舵暟鐩稿悓锛屾墍浠ュ畠鏄氳В锛泍=卤1锛寉'=0锛屾樉鐒舵弧瓒硑'2+y2-1=0锛屾晠y=卤1涔熸槸鍘熸柟绋嬬殑瑙(濂囪В)锛
绛旓細LZ锛岃繖棰樻尯绠鍗曠殑鍟婏紒绗竴闂細m涓巒骞宠鍒欐湁4sin^2(B+C)/2=cos2A+3.5锛孊+C+A=180搴 杩愮敤鍏紡cos(2X)=cos^2(X) -sin^2(X) =2cos^2(X)-1=1-2sin^2(X)灏嗕笂寮忚浆鍖栦负cosA鐨勭瓑寮忥紝姹傚嚭A锛涓轰粈涔瑕佸寲鎴恈osA鑰屼笉鏄痵inA鍛紵鍥犱负A鐨勮寖鍥翠负0-180锛岃嫢sinA姹傚嚭鏉ヤ负姝ｆ暟锛孉鐨勮搴︿笉...
