Question

prove that: cosA/1 - sinA = 1 + sinA/cosA​

Answer 1

Step-by-step explanation:

$r.h.s = \frac{1 + sin \: a}{cos \: a} \: \\ l.h.s = \: \frac{cos \: a}{1 - sin \: a} \\ = \frac{cos \: a \: }{1 - sin \: a} \times \frac{1 + sin \: a}{1 + sin \: a} \\ = \frac{cos \: a(1 + sin \: a)}{1 - {sin}^{2} a} \\ = \frac{cos \: a(1 + sin \: a)}{ {cos}^{2} a} \\ = \frac{1 + sin \: a}{cos \: a} \\ l.h.s \: = r.h.s$