化简求值:sin(π/4-3x)*cos(π/3-3x)-cos(π/6 3x)*sin(π/4 3x)
岳莪耐你 | 2010-03-31
我没分了!拜托!明天要交!
=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