计算:sinπ/12 sin5π/12

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计算:sinπ/12sin5π/12计算:sinπ/12sin5π/12计算:sinπ/12sin5π/12原式=sin(π/4-π/6)sin(π/4+sinπ/6)=(sinπ/4cosπ/6-c

计算:sinπ/12 sin5π/12
计算:sinπ/12 sin5π/12

计算:sinπ/12 sin5π/12
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