Question

cosA / 1-sinA=1+sinA/cosA​

Answer 1

cosA/1-sinA×1+sinA/1+sinA

cosA(1+sinA)/1-sin^2A

cosA(1+sinA)/cos^2A

1+sinA/cosA

proved

Answer 2

$\frac{ \cos(A) }{1 - \sin(A) } = \frac{1 + \sin(A) }{ \cos(A) } \\ = > \cos(A) \times \cos(A) = (1 + \sin(A)) \times (1 - \sin(A)) \\ =>{ cos }^{2} A = {1}^{2} - {sin}^{2} A \\ =>{ cos }^{2} A= 1 - {sin}^{2} A \\ => {cos}^{2} A = {cos}^{2} A$As, sin²A+cos²A=1 => cos²A= 1- sin² A

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