化简sin(π/3+α)+sin(π/3-α)如题

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化简sin(π/3+α)+sin(π/3-α)如题化简sin(π/3+α)+sin(π/3-α)如题化简sin(π/3+α)+sin(π/3-α)如题这个可以用和差化积的,只不过要先用诱导公式变一下:

化简sin(π/3+α)+sin(π/3-α)如题
化简sin(π/3+α)+sin(π/3-α)
如题

化简sin(π/3+α)+sin(π/3-α)如题
这个可以用和差化积的,只不过要先用诱导公式变一下:
比如说都变成sin的
原式=sin(π/6-α)+sin(π/6+α)
=2sin0.5*[(π/6-α)+(π/6+α)] cos0.5[(π/6-α)-(π/6+α)]
=2sin π/6 cosα
=cosα

罪(π/ 2 +α)+ COS(π/ 3 +α)
= COS(π/2-π/2-α)+cosπ/ 3COSα-sinπ/ 3sinα
=COSα +1 / 2COSα-√3/2sinsα
= 3/2COSα-√3/2sinsα
=√3(√3/2cosα-1/2sinα)
=√ 3(cosπ/ 6COSα-sinπ/ 6sinα)
=√3cos(π/ 6 +α)
(角差角公式的利用和转化)