cos2A-cos2B-cos2C=-1+4cosAcosBcosC
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Cos2A-Cos2B-Cos2C
=-2Sin(A+B)Sin(A-B)-1+2Sin²C
A+B+C=π
A+B=π-C
=-2Sin(π-C)Sin(A-B)-Cos2C
=-2SinCSin(A-B)-1+2Sin²C
=-2SinC[Sin(A-B)-SinC]-1
=-2SinC[Sin(A-B)-Sin(π-(A+B)]-1
=-2SinC[Sin(A-B)-Sin(A+B)]-1
=-2SinC[-2CosASinB]-1
=-4CosASinBSinC-1
=-1-4CosASinBSinC
=-2Sin(A+B)Sin(A-B)-1+2Sin²C
A+B+C=π
A+B=π-C
=-2Sin(π-C)Sin(A-B)-Cos2C
=-2SinCSin(A-B)-1+2Sin²C
=-2SinC[Sin(A-B)-SinC]-1
=-2SinC[Sin(A-B)-Sin(π-(A+B)]-1
=-2SinC[Sin(A-B)-Sin(A+B)]-1
=-2SinC[-2CosASinB]-1
=-4CosASinBSinC-1
=-1-4CosASinBSinC
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