Prove that^{ 1}/_{2 }tan (^{x}/_{2})+^{1}/_{4}tan(^{x}/_{4})+...+(^{1}/_{2n })tan (^{x}/_{2n })=(^{1}/_{2n })cot(^{x}/_{2} ^{ n }) - cotx for all n (- N and 0<x<(^{pi}/_{2}).

^{ 1}/_{2 }tan (^{x}/_{2})+^{1}/_{4}tan(^{x}/_{4})+...+(^{1}/_{2n })tan (^{x}/_{2n })=(^{1}/_{2n })cot(^{x}/_{2} ^{ n }) - cotx for all n (- N and 0<x<(^{pi}/_{2}).

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