Cot^2A(secA-1)/1+sinA=sec^2A*(1-sinA/1+secA. Prove this
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CRM
LHS
✌✌cot²A(secA-1)/(1+sinA)
✌✌{(cos²A/sin²A)(1/cosA-1)}/(1+sinA)
✌✌[{cos²A/(1-cos²A)}{(1-cosA)/cosA}]/(1+sinA)
✌✌[{cos²A/(1+cosA)(1-cosA)}×{(1-cosA)cosA}]/(1+sinA)
✌✌{cosA/(1+cosA)}/(1+sinA)
✌✌cosA/(1+sinA)(1+cosA)
RHS
✌✌sec²A(1-sinA)/(1+secA)
✌✌(1/cos²A)(1-sinA)/(1+1/cosA)
✌✌{(1-sinA)/cos²A}/{(1+cosA)/cosA}
✌✌{(1-sinA)/(1-sin²A)}/{(1+cosA)/cosA}
✌✌{(1-sinA)/(1+sinA)(1-sinA)}/{(1+cosA)/cosA}
✌✌{1/(1+sinA)}/{(1+cosA)/cosA}
✌✌cosA/(1+sinA)(1+cosA)
∴ LHS=RHS
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