cosA/(1-sinA) * (1+sinA)/(1+sinA)
= cosA(1+sinA)/(1-sin^2A)
= cosA(1+sinA)/cos^2A
= (1+sinA)/cosA
= secA + tanA
You can easily see that your original equation is false. Just use A = pi/4
prove that cosA/1-sinA=2cosecA
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