sin(2a＋π/3)＋sin(2a－π/3)化简急用呢

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sin(2a＋π/3)＋sin(2a－π/3)化简急用呢

sin(2a＋π/3)＋sin(2a－π/3)化简急用呢
sin(2a＋π/3)＋sin(2a－π/3)化简
急用呢

sin(2a＋π/3)＋sin(2a－π/3)化简急用呢
sin（2 a + π / 3）+ sin（2 a - π / 3）
= sin 2 a cos π / 3 + cos 2 a sin π / 3 + sin 2 a cos π / 3 - cos 2 a sin π / 3
= 2 sin 2a cos π / 3
= 2 × （1 / 2）sin 2a
= sin 2 a
参考公式：
sin(A+B) = sinAcosB+cosAsinB

sin(A-B) = sinAcosB-cosAsinB
参考资料：http://zhidao.baidu.com/question/88193418.html

sin(2a+π/3)=sin2acosπ/3+sinπ/3cos2a
sin(2a-π/3)=sin2acosπ/3-sinπ/3cos2a
两式相加的2sin2acosπ/3=sin2a=2sinacosa
主要是公式的应用 需要死记
sin(a+b)=sinacosb+sinbcosa
sin(a-b)=sinacosb-sinbcosa

sin(2a＋π/3)＋sin(2a－π/3)
=sin2acosπ/3+sinπ/3cos2a+sin2acosπ/3-sinπ/3cos2a
=2sin2acosπ/3
=sin2a

sin(2a＋π/3)＋sin(2a－π/3)
=(sin2a *cosπ/3 +cos2a *sinπ/3)+(sin2a *cos-π/3 +cos2a *sin-π/3)
=sin2a /2 +√3 cos2a /2+sin2a /2 -√3 cos2a /2
=sin2a

就直接把他化简开来。原式=2sin2α乘cos三分之π=2sin2α=2sinacosa

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