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化简tanx+cotx=2sinxcosx+sin3xsecx+cos3xcscx~
题目详情
化简 tanx+cotx=2sinxcosx+sin3xsecx+cos3xcscx~
▼优质解答
答案和解析
tanx+cotx＝1/sinxcosx
2sinxcosx+sin3xsecx+cos3xcscx
=2sinxcosx+sin(x+2x)/cosx+cos(x+2x)/sinx
=2sinxcosx+(sinxcos2x+cosxsin2x)/cosx+(cosxcos2x-sinxsin2x)/sinx
=2sinxcosx+sinxcos2x/cosx+sin2x+cosxcos2x/sinx-sin2x
=2sinxcosx+sinxcos2x/cosx+cosxcos2x/sinx
=2sinxcosx+（sinx^2cos2x+cosx^2cos2x）/sinxcosx
=2sinxcosx+（sinx^2+cosx^2）cos2x/sinxcosx
=2sinxcosx+cos2x/sinxcosx
…………你这题有误
如：x=45`,左＝2,右＝1+1－1…………
2sinxcosx+sin3xsecx+cos3xcscx
=2sinxcosx+sin(x+2x)/cosx+cos(x+2x)/sinx
=2sinxcosx+(sinxcos2x+cosxsin2x)/cosx+(cosxcos2x-sinxsin2x)/sinx
=2sinxcosx+sinxcos2x/cosx+sin2x+cosxcos2x/sinx-sin2x
=2sinxcosx+sinxcos2x/cosx+cosxcos2x/sinx
=2sinxcosx+（sinx^2cos2x+cosx^2cos2x）/sinxcosx
=2sinxcosx+（sinx^2+cosx^2）cos2x/sinxcosx
=2sinxcosx+cos2x/sinxcosx
…………你这题有误
如：x=45`,左＝2,右＝1+1－1…………
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