cos(2A)+cos(2C)=0怎么得出2cos(A+C)cos(A-C)=0

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cos(2A)+cos(2C)=0怎么得出2cos(A+C)cos(A-C)=0

cos(2A)+cos(2C)=0怎么得出2cos(A+C)cos(A-C)=0
cos(2A)+cos(2C)=0怎么得出2cos(A+C)cos(A-C)=0

cos(2A)+cos(2C)=0怎么得出2cos(A+C)cos(A-C)=0
将2A=(A+C)+(A-C),2C=(A+C)-(A-C)代入原式,
按两角和(差)的余弦公式展开,即可得到.

答:根据公式cosθ+cosφ=2cos[(θ+φ)/2]cos[(θ-φ)/2]
得到:
cos2A+cos2C=2cos[(2A+2C)/2]cos[(2A-2C)/2]
=2cos(A+C)cos(A-C)
所以:cos(2A)+cos(2C)=0可以得出2cos(A+C)cos(A-C)=0

cos(2A)+cos(2C)=0
cos(2A)=-cos(2C)
角2A+角2C=180
角A+角C=90
cos90=0
所以
2cos(A+C)cos(A-C)=0

因为2A=(A+C)+(A-C)
2C=(A+C)-(A-C)
cos2A=cos((A+C)+(A-C))=cos(A+C)cos(A-C)-sin(A+C)sin(A-C)
cos2C=cos((A+C)-(A-C))=cos(A+C)cos(A-C)+sin(A+C)sin(A-C)
两式相加得2cos(A+C)cos(A-C)=0

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