sin 2x为何等于2sinxcosx

cos^2-sin^2x+2sinxcosx\u4e3a\u4ec0\u4e48\u7b49\u4e8ecos2x-sin2x

cos2x-sin2x=(cosx)^2-(sinx)^2-2sinxcosx
\u6240\u4ee5\u524d\u9762\u7684\u5f0f\u5b50\u53ef\u80fd\u7b26\u53f7\u6253\u9519\u4e86~
\u5e0c\u671b\u53ef\u4ee5\u5e2e\u5f97\u5230\u4f60~

\uff081\uff09\u4f60\u77e5\u9053\u4e8c\u500d\u89d2\u516c\u5f0f\u5417\uff1fsin2x=2sinxcosx\uff0c\u53d8\u5f62\u5f97\uff1asinxcosx=1/2 sin2x
\uff082\uff09\u4e8c\u500d\u89d2\u516c\u5f0f\u7684\u6765\u6e90\uff1asin(a+b)=sinacosb+cosasinb,\u4ee4a=b=x,
\u5219\u6709sin\uff08x+x\uff09=sinxcosx+cosxsinx=2sinxcosx=sin2x.

2x=x+x
sin2x=sin(x+x)
正弦两角和公式：sin(a+b)=sinacosb+cosasinb
所以sin(x+x)=sinxcosx+cosxsinx=2sinxcosx

sin2x=sin(x+x)=sinxcosx+cosxsinx=2sinxcosx

扩展阅读：freedom+is+not+free ... sin2x 极限为啥是2x ... ∫0 in2 2xe∧x∧2dx ... sin计算器在线计算 ... sin 2xcos 2x ... sin与cos的转换公式大全 ... sin x 2 dx ... sin5xsin7x ... y等于2sin2x图像 ...