作业帮(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)的值 急!
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(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)的值 急!
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)的值 急!
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)的值 急!
解一
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)
=2cosπ/4*sinπ/6*2sinπ/4*cosπ/6 用和差化积
=sinπ/2*sinπ/3 用正弦函数二倍角公式
=√3/2
解二
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)
=(sin²5π/12-sin²π/12) 化为二数平方差
=1/2*(1-cos5π/6)-1/2*(1-cosπ/6) 用余弦函数的二倍角公式
=cosπ/6
=√3/2
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)
=(cosπ/12-sinπ/12)(cosπ/12+sinπ/12)
=cos^2π/12-sin^2π/12
=cosπ/6
=√3/2
原式=sin^2(5/12π)-sin^2(1/12π)
=1/2(1-cos5/6π)-1/2(1-cos1/6π)
=根号3/2
计算：sinπ／12 sin5π／12
(sin5π/12-sinπ/12)(sin5π/12+sinπ/12)的值 急!
(sinπ/12)-(sin5π/12)+(2sinπ/8)(sin3π/8)
sinπ/12-sin5π/12+2sinπ/8sin3π/8
(sin5π/12+cos5π/12)(sinπ/12-cosπ/12)
(sin5π/12-sinπ/12)(cos5π/12+cosπ/12)=?
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