Prove the identity? (1+tanx) / (1+cotx) = (1-tanx) / (cotx-1)?

Right side is cot(x) - sin(x) cos(x)/sin(x) - sin(x)/cos(x) (cos^2(x)-sin^2(x))/(sin(x)cos(x) (cos^2(x)-(1-cos^2(x))/(sin(x)cos(x) (2cos^2x-1)/(sin(x)cos(x)) QED.

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