For an acute angle A, $\sqrt{\frac{1+\sin A}{1-\sin A}}$ equals which expression?

Multiply numerator and denominator inside the root by $1+\sin A:\sqrt{\frac{(1+\sin A{)}^2}{1-{\sin }^{2}A}}=\sqrt{\frac{(1+\sin A{)}^2}{{\cos }^{2}A}}=\frac{1+\sin A}{\cos A}=\sec A+\tan A$, positive because A is acute. Multiplying by $1-\sin A$ instead gives $\sec A-\tan A$, which is the RECIPROCAL of the required value, not the value.