sin5/12π*cosπ/12 怎么算

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sin5/12π*cosπ/12 怎么算
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sin5/12π*cosπ/12 怎么算
sin5/12π*cosπ/12 怎么算

sin5/12π*cosπ/12 怎么算
sin(1/4π + 1/6π)×cos(1/4π -1/6π)然后用正弦余弦的和角差角公式算就行了

sin5/12π=sin(π/4+π/6)=sinπ/4cosπ/6+cosπ/4sinπ/6=√2/2 (√3/2+1/2)
cosπ/12=sin(π/2-π/12)=sin5π/12=√2/2 (√3/2+1/2)
sin5/12π*cosπ/12 =[√2/2 (√3/2+1/2)]^2=1/2+√3/4