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Prove (1+cotA+tanA)(sinA-cosA)=sinAtanA-...

Prove `(1+cotA+tanA)(sinA-cosA)=sinAtanA-cotAcosA`

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Prove that: cotA/2-tanA/2=(cosA/2)/(sinA/2)-(sinA/2)/(cosA/2) =(cos^(2)A/2-sin^(2)A/2)/(sinA/2cosA/2) =cosA/(1/2.(2sinA/2cosA/2)) =(2cosA)/(sinA)=2cotA = RHS. Hence Proved.