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prove that sin A(1+tan A)+cos A(1+cot A)= sec A+ cosec A

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    multiply the left side by sinAcosA/(sinAcosA)

    sin^2A*(cosA+sinA)+cos^2A*(sin+cosA)/ ( )

    (cosA+sinA)(sin^2+ cos^2)/ ( )

    1/sinA + 1/Cos A

    cscA + secA

    qed

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