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在△ABC中cosBcosC=3sinBsinC试求：cosA/cos(B-C)
题目详情
在△ABC中cosBcosC=3sinBsinC 试求：cosA/cos(B-C)
▼优质解答
答案和解析
cosA=cos(180-B-C)
=-cos(B+C)
=-(cosBcosC-sinBsinC)
=-(3sinBsinC-sinBsinC)
=-2sinBsinC
cos(B-C)=cosBcosC+sinBsinC
=3sinBsinC+sinBsinC
=4sinBsinC
cosA/cos(B-C)
=-2sinBsinC/4sinBsinC
=-1/2
=-cos(B+C)
=-(cosBcosC-sinBsinC)
=-(3sinBsinC-sinBsinC)
=-2sinBsinC
cos(B-C)=cosBcosC+sinBsinC
=3sinBsinC+sinBsinC
=4sinBsinC
cosA/cos(B-C)
=-2sinBsinC/4sinBsinC
=-1/2
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