为何1-cosx等价无穷小？ 1-cosx等于什么等价无穷小?
1-cosx\u7b49\u4ef7\u65e0\u7a77\u5c0f\u4e8e\u4ec0\u4e48?\u4e3a\u4ec0\u4e48\uff1f\u7b54\uff1a
\u7528\u4e8c\u500d\u89d2\u516c\u5f0f\uff1a
cos2a=1-2sin²a
1-cos2a=2sin²a
\u6240\u4ee5\uff1a
1-cosx=2sin²(x/2)~2\u00d7(x/2)²~x²/2
\u6240\u4ee5\uff1a
1-cosx\u7684\u7b49\u4ef7\u65e0\u7a77\u5c0f\u4e3ax²/2
\u7b49\u4ef7\u65e0\u7a77\u5c0f\u662f\u65e0\u7a77\u5c0f\u4e4b\u95f4\u7684\u4e00\u79cd\u5173\u7cfb\uff0c\u6307\u7684\u662f\uff1a\u5728\u540c\u4e00\u81ea\u53d8\u91cf\u7684\u8d8b\u5411\u8fc7\u7a0b\u4e2d\uff0c\u82e5\u4e24\u4e2a\u65e0\u7a77\u5c0f\u4e4b\u6bd4\u7684\u6781\u9650\u4e3a1\uff0c\u5219\u79f0\u8fd9\u4e24\u4e2a\u65e0\u7a77\u5c0f\u662f\u7b49\u4ef7\u7684\u3002
\u6781\u9650
\u6570\u5b66\u5206\u6790\u7684\u57fa\u7840\u6982\u5ff5\u3002\u5b83\u6307\u7684\u662f\u53d8\u91cf\u5728\u4e00\u5b9a\u7684\u53d8\u5316\u8fc7\u7a0b\u4e2d\uff0c\u4ece\u603b\u7684\u6765\u8bf4\u9010\u6e10\u7a33\u5b9a\u7684\u8fd9\u6837\u4e00\u79cd\u53d8\u5316\u8d8b\u52bf\u4ee5\u53ca\u6240\u8d8b\u5411\u7684\u6570\u503c(\u6781\u9650\u503c)\u3002\u6781\u9650\u65b9\u6cd5\u662f\u6570\u5b66\u5206\u6790\u7528\u4ee5\u7814\u7a76\u51fd\u6570\u7684\u57fa\u672c\u65b9\u6cd5\uff0c\u5206\u6790\u7684\u5404\u79cd\u57fa\u672c\u6982\u5ff5(\u8fde\u7eed\u3001\u5fae\u5206\u3001\u79ef\u5206\u548c\u7ea7\u6570)\u90fd\u662f\u5efa\u7acb\u5728\u6781\u9650\u6982\u5ff5\u7684\u57fa\u7840\u4e4b\u4e0a\u3002
\u7136\u540e\u624d\u6709\u5206\u6790\u7684\u5168\u90e8\u7406\u8bba\u3001\u8ba1\u7b97\u548c\u5e94\u7528.\u6240\u4ee5\u6781\u9650\u6982\u5ff5\u7684\u7cbe\u786e\u5b9a\u4e49\u662f\u5341\u5206\u5fc5\u8981\u7684\uff0c\u5b83\u662f\u6d89\u53ca\u5206\u6790\u7684\u7406\u8bba\u548c\u8ba1\u7b97\u662f\u5426\u53ef\u9760\u7684\u6839\u672c\u95ee\u9898\u3002\u5386\u53f2\u4e0a\u662f\u67ef\u897f(Cauchy\uff0cA.-L.)\u9996\u5148\u8f83\u4e3a\u660e\u786e\u5730\u7ed9\u51fa\u4e86\u6781\u9650\u7684\u4e00\u822c\u5b9a\u4e49\u3002
1-cosx\u7b49\u4e8ex²/2\u7b49\u4ef7\u65e0\u7a77\u5c0f\u3002
\u5177\u4f53\u56de\u7b54\u5982\u4e0b\uff1a
\u56e0\u4e3a\uff1a
cos2a=1-2sin²a
1-cos2a=2sin²a
\u6240\u4ee5\uff1a
1-cosx=2sin²(x/2)~2\u00d7(x/2)²~x²/2
\u6240\u4ee51-cosx\u7b49\u4e8ex²/2\u7b49\u4ef7\u65e0\u7a77\u5c0f\u3002
\u500d\u89d2\u534a\u89d2\u516c\u5f0f\uff1a
sin ( 2\u03b1 ) = 2sin\u03b1 \u00b7 cos\u03b1
sin ( 3\u03b1 ) = 3sin\u03b1 - 4sin & sup3 ; ( \u03b1 ) = 4sin\u03b1 \u00b7 sin ( 60 + \u03b1 ) sin ( 60 - \u03b1 )
sin ( \u03b1 / 2 ) = \u00b1 \u221a( ( 1 - cos\u03b1 ) / 2)
\u7531\u6cf0\u52d2\u7ea7\u6570\u5f97\u51fa\uff1a
sinx = [ e ^ ( ix ) - e ^ ( - ix ) ] / ( 2i )
\u7ea7\u6570\u5c55\u5f00\uff1a
sin x = x - x3 / 3! + x5 / 5! - ... ( - 1 ) k - 1 * x 2 k - 1 / ( 2k - 1 ) ! + ... ( - \u221e < x < \u221e )
\u5bfc\u6570\uff1a
\uff08 sinx \uff09 ' = cosx
\uff08 cosx ) ' = \ufe63 sinx
方法如下，请作参考：
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1-cosx等于x²/2等价无穷小。
具体回答如下：
因为：
cos2a=1-2sin²a
1-cos2a=2sin²a
所以：
1-cosx=2sin²(x/2)~2×(x/2)²~x²/2
所以1-cosx等于x²/2等价无穷小。
倍角半角公式：
sin ( 2α ) = 2sinα · cosα
sin ( 3α ) = 3sinα - 4sin & sup3 ; ( α ) = 4sinα · sin ( 60 + α ) sin ( 60 - α )
sin ( α / 2 ) = ± √( ( 1 - cosα ) / 2)
由泰勒级数得出：
sinx = [ e ^ ( ix ) - e ^ ( - ix ) ] / ( 2i )
级数展开：
sin x = x - x3 / 3! + x5 / 5! - ... ( - 1 ) k - 1 * x 2 k - 1 / ( 2k - 1 ) ! + ... ( - ∞ < x < ∞ )
导数：
（ sinx ） ' = cosx
（ cosx ) ' = ﹣ sinx
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