cos2A/a²-cos2B/b²=1/a²-1/b²

cos2Aa2-cos2Bb2=2cos2A-1a2-cos2B-1b2  Using cos2A=2cos2A-1;cos2B=2cos2B-1 Now applying cos ruleCosA=b2+c2-a22bc;CosB=a2+c2-b22ac=2b2+c2-a22bc2-1a2-2a2+c2-b22ac2-1b2=b2+c2-a22-2b2c22a2b2c2-a2+c2-b22-2a2c22a2b2c2=b4+c4+2b2c2+a4-2a2b2+c2-2b2c2-a4+c4+b4+2a2c2-2b2a2+c2-2a2c22a2b2c2=b4+c4+2b2c2+a4-2a2b2-2a2c2-2b2c2-a4+c4+b4+2a2c2-2b2a2-2b2c2-2a2c22a2b2c2=2b2c2-2a2c22a2b2c2=1a2-1b2  Hence proved

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