cos2α和sin2α之间怎么互换?

\u6c42\u8bc1: Sin2\u03b1\uff0bsin2\u03b2\uff0dSin2\u03b1\u00d7sin2\u03b2\uff0bcos2\u03b1\u00d7 cos2\u03b2\uff1d1

\u4ee5\u4e0a\u76842\u90fd\u662f\u5e73\u65b9\u5427
\u89e3\uff1asin2\u03b1+sin2\u03b2-sin2\u03b1sin2\u03b2+cos2\u03b1cos2\u03b2
=sin2\u03b1\uff081-sin2\u03b2\uff09+sin2\u03b2+cos2\u03b1cos2\u03b2
=sin2\u03b1•cos2\u03b2+sin2\u03b2+cos2\u03b1cos2\u03b2
=cos2\u03b2\uff08sin2\u03b1+cos2\u03b1\uff09+sin2\u03b2
=cos2\u03b2+sin2\u03b2=1

Sin2\u03b1\uff0bsin2\u03b2\uff0dSin2\u03b1\u00d7sin2\u03b2\uff0bcos2\u03b1\u00d7 cos2\u03b2
=Sin2\u03b1\uff0bsin2\u03b2-4Sin\u03b1cos\u03b1sin\u03b2 cos\u03b2+(cos^\u03b1-Sin^\u03b1)\u00d7 (cos^\u03b2-Sin^\u03b2)
=Sin2\u03b1+sin2\u03b2+(cos\u03b1cos\u03b2-Sin\u03b1Sin\u03b2)^-(cos\u03b1Sin\u03b2+Sin\u03b1cos\u03b2)^
=Sin2\u03b1+sin2\u03b2+cos^(\u03b1+\u03b2)-Sin^(\u03b1+\u03b2)
=1+Sin2\u03b1+sin2\u03b2-2Sin^(\u03b1+\u03b2)
=1+2(Sin\u03b1cos\u03b1+Sin\u03b2cos\u03b2-Sin\u03b1cos\u03b1-Sin\u03b2cos\u03b2)
=1

cos^2(2a)+sin^2(2a)=1 cos(2a)=[1-sin^2(2a)]^1/2

它们的平方值相加等于1
然后开方就行了

cos2伪=cos²伪-sin²伪=1-2sin²=2cos²-1鐨勬帹绠楄繃绋媉鐧惧害鐭 ...
绛旓細cos2伪=cos(伪+伪)=cos伪cos伪 - sin伪sin伪 =cos²伪 - sin²伪 =cos²伪 - (1 - cos²伪)=cos²伪 - 1 + cos²伪 =2cos²伪 - 1 鎴栬=(1 - sin²伪) - sin²伪 =1 - sin²伪 - sin²伪 =1 - 2sin&#...

sin2伪+cos2伪鎬庝箞鍙樻垚鍚屽悕涓夎鍑芥暟
绛旓細濡傚浘鎵绀猴細

璇烽棶sin伪鍜宑os伪鎬庝箞鐩镐簰杞寲?
绛旓細+ cos^2伪 卤 2sin伪cos伪 = 1 卤 2sin伪cos伪 鈭磗in伪卤cos伪 = 卤鈭(1 卤 2sin伪cos伪)鍊掓暟鍏崇郴锛歴ina*csca=1 cosa*seca=1 tana*cota=1 鍟嗘暟鍏崇郴锛歵ana=sina/cosa ctga=cosa/sina 骞虫柟鍏崇郴锛(sina)^2+(cosa)^2=1 1+(tana)^2=(seca)^2 1+(cota)^2=(csca)^2 ...

鍊嶈鍏紡cos2伪=cos^2(伪)-sin^2(伪)=2cos^2(伪)-1=1-2sin^2(伪)鎬庝箞...
绛旓細鍏紡cos(x+y)=cosxcosy-sinxsiny cos2a=cos(a+a)=cosa脳cosa-sina脳sina=cos²a-sin²a=cos²a-(1-cos²a)=2cos²a-1 =(2-2sin²a)-1=1-2sin²a

涓轰粈涔sin2伪 =2sin伪 cos伪 ?绫讳技浜庤繖鏍风殑鍏紡杩樻湁鍝簺?
绛旓細鍊掓暟鍏崇郴: tan伪 路cot伪=1 sin伪 路csc伪=1 cos伪 路sec伪=1 鍟嗙殑鍏崇郴: sin伪/cos伪=tan伪=sec伪/csc伪 cos伪/sin伪=cot伪=csc伪/sec伪 骞虫柟鍏崇郴: sin^2(伪)+cos^2(伪)=1 1+tan^2(伪)=sec^2(伪) 1+cot^2(伪)=csc^2(伪)骞冲父閽堝涓嶅悓鏉′欢鐨勫父鐢ㄧ殑涓や釜鍏紡 sin² 伪+cos² 伪...

鐭ラ亾sin2伪鎬庝箞姹cos2伪
绛旓細鏍规嵁sin²2伪 + cos²2伪=1 鐒跺悗鍐嶆牴鎹辩殑鑼冨洿锛岀‘瀹cos2伪鐨勬璐

sin²伪=(1-cos(2伪))/2鍜宻in²伪=(1-sin(2伪))/2 鍒嗗埆鏄粈涔堝叕寮...
绛旓細=1-2sin²a 鎵浠2sin²a=1-cos2a 浜﹀嵆sin²a=(1-cos2a)/2 鈶os2a =cos²a-sin²a =cos²a-(1-cos²a)=2cos²a-1 鎵浠2cos²a=1+cos2a 浜﹀嵆cos²a=(1+cos2a)/2 鑰宻in2a=2sinacosa 杩欎釜 sin²伪=锛1-sin锛2...

sin2伪=2sin伪cos伪 杩欎釜涓ゅ嶈鍏紡鏄鎬庝箞鎺ㄥ鏉ョ殑?鑳戒笉鑳界敾涓涓笁瑙...
绛旓細杩欎釜鍏紡鏉ユ簮浜庢寮︾殑鍜岃鍏紡 sin(伪+尾)=sin伪cos尾+cos伪sin尾,浠庝笅鍥惧彲浠ョ洿鎺ョ湅鍑烘潵瀵逛簬浠绘剰閿愯伪+尾,鍏紡鎴愮珛 瀹為檯涓婅繖涓叕寮忓浠绘剰瑙掗兘鎴愮珛,浣嗕换鎰忚鏃犳硶鍦ㄤ笁瑙掑舰涓綋鐜

(cos2伪-sin2伪)/(cos2伪+sin2伪)=(1-tan2伪)/(1+tan2伪)鏄鎬庝箞鍙樼殑...
绛旓細锛cos2伪-sin2伪锛/锛坈os2伪+sin2伪锛夊垎瀛愬垎姣嶅悓闄os2伪锛歔锛坈os2伪-sin2伪锛壝穋os2伪]/[锛坈os2伪+sin2伪锛塢梅cos2伪 =锛1-sin2伪梅cos2伪锛/锛1+sin2伪梅cos2伪锛夊洜涓簊in2伪梅cos2伪=tan2伪 鎵浠 锛坈os2伪-sin2伪锛/锛坈os2伪+sin2伪锛=锛1-tan2伪锛/锛1+tan2伪锛夐...

甯繖瑙ｄ笅杩欓亾棰,涓嶇煡閬cos2伪鏄鎬庝箞鍙樻垚-sin2(伪-4鍒嗕箣蟺)
绛旓細鍥犱负杩欓噷涔﹀啓涓嶄究锛屾晠灏嗘垜鐨勭瓟妗堝仛鎴愬浘鍍忚创浜庝笅鏂癸紝璋ㄤ緵妤间富鍙傝冿紙鑻ュ浘鍍忔樉绀鸿繃灏忥紝鐐瑰嚮鍥剧墖鍙斁澶э級銆

扩展阅读：sin2a+cos2a始终如一 ... sinα与cosα怎么互换 ... sin2α cos2α 1 ... sin tan cos三角函数表 ... 1+cos2α ... cos2a公式大全 ... cos三角函数公式大全 ... cos2a与tana的转化 ... asinx十bcosx万能公式 ...