sin2x等于2sinxcosx怎么来的 sin2x=2sinxcosx怎么推导出来的？？
2sinxcosx\u4e3a\u4ec0\u4e48\u7b49\u4e8esin2x \u6839\u636e\u7684\u662f\u4ec0\u4e48\u516c\u5f0f\u56e0\u4e3a2sinxcosx =sinxcosx +cosxsinx=sin(x+x)=sin2x
\u6839\u636e\u4ee5\u4e0b\u516c\u5f0f\uff1a
\u8fd0\u7528\u4e24\u89d2\u548c\u4e0e\u5dee\u516c\u5f0f\u5373\u53ef\u8bc1\u660e\uff0c\u5177\u4f53\u516c\u5f0f\u4ecb\u7ecd\u5982\u4e0b\uff1a
1\u3001sin(A+B)=sinAcosB+cosAsinB\uff1b
2\u3001sin(A-B)=sinAcosB-sinBcosA\uff1b
3\u3001cos(A+B)=cosAcosB-sinAsinB\uff1b
4\u3001cos(A-B)=cosAcosB+sinAsinB\uff1b
5\u3001tan(A+B)=(tanA+tanB)/(1-tanAtanB)\uff1b
6\u3001tan(A-B)=(tanA-tanB)/(1+tanAtanB)\uff1b
7\u3001ctg(A+B)=(ctgActgB-1)/(ctgB+ctgA)\uff1b
\u6269\u5c55\u8d44\u6599
\u4e09\u89d2\u51fd\u6570\u7684\u6700\u503c\u95ee\u9898\u662f\u5bf9\u4e09\u89d2\u51fd\u6570\u7684\u6982\u5ff5\u3001\u56fe\u8c61\u4e0e\u6027\u8d28\u4ee5\u53ca\u8bf1\u5bfc\u516c\u5f0f\u3001\u540c\u89d2\u95f4\u7684\u57fa\u672c\u5173\u7cfb\u3001\u4e24\u89d2\u7684\u548c\u4e0e\u5dee\u516c\u5f0f\u7684\u7efc\u5408\u8003\u67e5\uff0c\u4e5f\u662f\u51fd\u6570\u601d\u60f3\u7684\u5177\u4f53\u4f53\u73b0\u3002
\u89e3\u51b3\u4e09\u89d2\u51fd\u6570\u7684\u6700\u503c\u95ee\u9898\u53ef\u901a\u8fc7\u9002\u5f53\u7684\u4e09\u89d2\u53d8\u6362\u6216\u4ee3\u6570\u6362\u5143\uff0c\u5316\u5f52\u4e3a\u67d0\u79cd\u4e09\u89d2\u51fd\u6570\u6216\u4ee3\u6570\u51fd\u6570\uff0c\u518d\u5229\u7528\u4e09\u89d2\u51fd\u6570\u7684\u6709\u754c\u6027\u6216\u5e38\u7528\u7684\u6c42\u51fd\u6570\u6700\u503c\u7684\u65b9\u6cd5\u53bb\u5904\u7406\u3002
\u6781\u503c\u4e0e\u6700\u503c\u7684\u5173\u7cfb\uff1a
1\u3001\u5b9a\u4e49\u57df\u7aef\u70b9\u4e00\u5b9a\u4e0d\u662f\u6781\u503c\u70b9\uff0c\u7aef\u70b9\u7684\u51fd\u6570\u503c\u4e00\u5b9a\u4e0d\u662f\u6781\u503c\uff1b
2\u3001\u6781\u503c\u662f\u51fd\u6570\u5c40\u90e8\u6027\u8d28\uff0c\u662f\u5728\u5b9a\u4e49\u57df\u67d0\u4e00\u5c40\u90e8\u8303\u56f4\u5185\u7684\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\uff1b
3\u3001\u51fd\u6570\u7684\u6700\u5927\u503c\u4e3aMAX{\u6781\u503c\u3001\u8fb9\u754c\u51fd\u6570\u503c}\uff1b\u6700\u5c0f\u503c\u4e3aMIN{\u6781\u503c\u3001\u8fb9\u754c\u51fd\u6570\u503c}\u3002
sin(x+x)=sinxcosx+cosxsinx=2sinxcosx
cos(x+x)=cosxcosx-sinxsinx=(cosx)^2-(sinx)^2
\u53e6\u5916\u4e24\u4e2a\u5206\u522b\u52a0\u548c\u51cf1=(sinx)^2+(cosx)^2
sin2x=2sinxcos\u6839\u636esin(a+b)=sinacosb+cosasinb\u63a8\u51fa
cos2x=1-(2sinx)^2 or (2cosx)^2-1,\u540c\u7406\u7528
cos(a+b)=cosacosb-sinasinb\u63a8\u5bfc
sin2x
=sin(x+x)
=sinxcosx+cosxsinx
=2sinxcosx
cos2x
=cos(x+x)
=cosxcosx-sinxsinx
=cos^2x-sin^2x
tan2x
=tan(x+x)
=(tanx+tanx)/(1-tanxtanx)
=2tanx/(1-tan^2x)
=sinxcosx+cosxsinx
=2sinxcosx
绛旓細涓銆佷緷鎹細鍊嶈鍏紡锛sin2x=2sinxcosx 浜屻佸嶈鍏紡鎺ㄥ锛氬洜涓簊in(A+B)=sinAcosB+cosAsinB锛堜笁瑙掑嚱鏁帮級鎵浠in2A=2sinAcosA 涓夈佹敞锛氫笁瑙掑嚱鏁扮殑鎺ㄥ锛氶鍏堝缓绔嬬洿瑙掑潗鏍囩郴,鍦ㄧ洿瑙掑潗鏍囩郴xOy涓綔鍗曚綅鍦哋,骞朵綔鍑鸿a,b,涓-b,浣胯a鐨勫紑杈逛负Ox,浜ゅ渾O浜庣偣P1,缁堣竟浜ゅ渾O浜庣偣P2,瑙抌鐨勫杈逛负OP2,...
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绛旓細cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 - 1 = 1 - 2(sinx)^2 sin2x = 2sinxcosx 璇卞鍏紡鍙ｈ瘈鈥滃鍙樺伓涓嶅彉锛岀鍙风湅璞￠檺鈥濇剰涔夛細k脳蟺/2卤a(k鈭坺)鐨勪笁瑙掑嚱鏁板 锛1锛夊綋k涓哄伓鏁版椂锛绛変簬伪鐨勫悓鍚嶄笁瑙掑嚱鏁板硷紝鍓嶉潰鍔犱笂涓涓妸伪鐪嬩綔閿愯鏃跺師涓夎鍑芥暟鍊肩殑绗﹀彿锛涳紙2锛夊綋k涓...
绛旓細sin2x=2sinx cos x杩欎釜娌￠敊锛屼絾鏄篃绛変簬-cos(蟺/2+2x)锛岃繖涓槸姝ｇ‘鐨勩傁/2卤伪鍙3蟺/2卤伪涓幬辩殑涓夎鍑芥暟鍊间箣闂寸殑鍏崇郴锛堣繖浜涘叕寮忔渶濂借浣忥級锛歴in锛埾/2+伪锛=cos伪 cos锛埾/2+伪锛=锛峴in伪 tan锛埾/2+伪锛=锛峜ot伪 cot锛埾/2+伪锛=锛峵an伪 sin锛埾/2锛嵨憋級=cos伪 ...
绛旓細璁颁綇鍩烘湰鍏紡 sin2x=2sinxcosx 鎵浠ュ緱鍒(sinx)^2 *(cosx)^2 =1/4 *(2sinxcosx)^2 =1/4 *(sin2x)^2锛屽氨鏄綘瑕佺殑缁撴灉
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