cosA/(1 - sin A) is equal to
Expression : cosA/(1 - sin A)
Multiplying numerator and denominator by (1 + sin A)
= $$\frac{cos A}{1 - sin A} \times \frac{1 + sin A}{1 + sin A}$$
= $$\frac{cos A (1 + sin A)}{1 - sin^2 A}$$
= $$\frac{cos A (1 + sin A)}{cos^2 A} = \frac{1 + sin A}{cos A}$$
= $$\frac{1}{cos A} + \frac{sin A}{cos A} = sec A + tan A$$
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