Question

cotA+cosecA-1÷cotA-cosecA+1 = 1+cosA÷sinA

Answer 1

cot+cosec-1/cot-cosec+1 = 1+cos/sin

cot+cosec -[cosec2-cot2] / cot -cosec+1

cot+cosec-[(cosec+cot)(cosec-cot)] / cot-cosec+1         (a2-b2= a+b*a-b)

cot+cosec[1-cosec+cot] /cot-cosec+1        (taking cot+cosec common)

∴ cot+cosec= LHS

1+cos/sin = 1/sin + cos/sin
                = cosec+cot
                =cot+cosec=RHS      (1/sin = cosec & cos/sin = cot)

           LHS=RHS
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