计算:sin(兀)/(12) 乘以 sin(5兀)/(12)

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计算:sin(兀)/(12) 乘以 sin(5兀)/(12)

计算:sin(兀)/(12) 乘以 sin(5兀)/(12)
计算:sin(兀)/(12) 乘以 sin(5兀)/(12)

计算:sin(兀)/(12) 乘以 sin(5兀)/(12)
sin(π/12)*sin(5π/12)
=sin(π/12)*cos(π/12)
=sin(π/6)/2
=1/4
2倍角公式
sin2x=2sinxcosx

原式=sin(π/4-π/6)sin(π/4+sinπ/6)
=(sinπ/4cosπ/6-cosπ/4sinπ/6)(sinπ/4cosπ/6+cosπ/4sinπ/6)
=(sinπ/4cosπ/6)²-(cosπ/4sinπ/6)²
=(√6/4)²-(√2/4)²
=6/16-2/16
=1/4