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cot^2x-1/1+cot^2x=2Cos^2x-1

I startedon the Left side tring to prove the equation.

cot^2x-1/csc^2x using Pyth. Theory

(cot^2x/csc^2x)-(1/csc^2x) reciprocal Identites

((cos^2x/sin^2x)/csc^2x)-(sin^2x) reciprocal Identites

(cos^2x/sin^2x)*(sin^2x)-(sin^2x) //sin^2x will cancel outleaving

cos^2x - sin^2x this does not = 2Cos^2x -1

Could somone point me in the right direstion .Thank s in advanced Rada3b