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Verifying trig identities tan^2x-1/cot^2x-1 = 1-sec^2x

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LS : (tan^2 x - 1)/(cot^2 x - 1) = (sin^2 x/cos^2 x - 1)/(cos^2 x/sin^2 x - 1) = [(sin^2 x - cos^2 x)/cos^2 x] / [(cos^2 x - sin^2 x)/sin^2 x] = [(sin^2 x - cos^2 x) * sin^2 x] / [cos^2 x * (cos^2 x - sin^2 x)] = - sin^2 x / cos^2 x = - (1 - cos^2 x) / cos^2 x = (cos^2 x - 1) / cos^2 x = cos^2 x/cos^2 x - 1/cos^2 x = 1 - sec^2 x = 1 - sec^2 x : RS

            
        

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