How do you prove $cos(x) / (1-sin(x)) = sec(x) + tan(x)$ ?

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Answer 1 · 2018-03-17T05:27:33

Please refer to the Explanation.

We have, $cosx/(1-sinx)$ ,

$=cosx/(1-sinx)xx1$ ,

$=cosx/(1-sinx)xx(1+sinx)/(1+sinx)$ ,

$={cosx(1+sinx)}/{1-sin^2x)$ ,

$={cosx(1+sinx)}/cos^2x$ ,

$=(1+sinx)/cosx$ ,

$=1/cosx+sinx/cosx$ ,

$=secx+tanx$ , as desired!

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How do you prove cos(x) / (1-sin(x)) = sec(x) + tan(x)cos(x) / (1-sin(x)) = sec(x) + tan(x)?