类比“两角和与差的正余弦公式”的形式,对于给定的两个函数,S(x)=,C(x)=,其中a>0,且a≠1,下面正确的运算公式是
①S(x+y)=S(x)C(y)+C(x)S(y);②S(x-y)=S(x)C(y)-C(x)S(y);
③C(x+y)=C(x)C(y)-S(x)S(y);④C(x-y)=C(x)C(y)+S(x)S(y);A.①③B.②④C.①④D.①②③④
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D
解析分析:写出“两角和与差的正余弦公式”的形式,写出类比结论.
解答:∵“两角和与差的正余弦公式”的形式是sin(x+y)=sinxcosy+cosxsinysin(x-y)=sinxcosy-cosxsinycos(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsiny对于有类比结论S(x+y)=S(x)C(y)+C(x)S(y);S(x-y)=S(x)C(y)-C(x)S(y);C(x+y)=C(x)C(y)-S(x)S(y);C(x-y)=C(x)C(y)+S(x)S(y);故选D
点评:本题考查利用类比推理从形式上写出类比结论.写类比结论时:先找类比对象,再找类比元素.