化简求值:sin(π/4-3x)*cos(π/3-3x)-cos(π/6+3x)*sin(π/4+3x)
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/29 09:18:36
化简求值:sin(π/4-3x)*cos(π/3-3x)-cos(π/6+3x)*sin(π/4+3x)
=sin(π/4-3x)*cos(π/3-3x)-sin[π/2-(π/6+3x)]*cos[π/2-(π/4+3x)]
=sin(π/4-3x)*cos(π/3-3x)-sin(π/3-3x)*cos(π/4-3x)
由正弦函数两角和差公式得
=sin[(π/4-3x)-(π/3-3x)]
=sin(-π/12)
= -sin(π/12)
= -√{[1-cos(π/6)]/2}
= -√[(1-√3/2)/2]
= -√{(1/2-√3/2)^2] /2}
= (1/2-√3/2)/√2
= √2/4 - √6/4
=sin(π/4-3x)*cos(π/3-3x)-sin(π/3-3x)*cos(π/4-3x)
由正弦函数两角和差公式得
=sin[(π/4-3x)-(π/3-3x)]
=sin(-π/12)
= -sin(π/12)
= -√{[1-cos(π/6)]/2}
= -√[(1-√3/2)/2]
= -√{(1/2-√3/2)^2] /2}
= (1/2-√3/2)/√2
= √2/4 - √6/4
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