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求下列各式的值cos7π/12.(2)cos(-61π/12)
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答案和解析
cos7π/12=cos(π/2+π/12)=-sinπ/12=-sin(π/3-π/4)=sinπ/4cosπ/3-sinπ/3cosπ/4
=√2/4(1-√3)=(√2-√6)/4
cos(-61π/12)=cos(61π/12)=cos(5π+π/12)=-cosπ/12=-cos(π/3-π/4)
=-cosπ/3cosπ/4-sinπ/3sinπ/4=-√2/4(1+√3)=-(√2+√6)/4
=√2/4(1-√3)=(√2-√6)/4
cos(-61π/12)=cos(61π/12)=cos(5π+π/12)=-cosπ/12=-cos(π/3-π/4)
=-cosπ/3cosπ/4-sinπ/3sinπ/4=-√2/4(1+√3)=-(√2+√6)/4
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