How do you verify $cosx/(1-sinx)= secx+tanx$ ?

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Answer 1 · 2015-08-20T13:00:30

$sec A = 1/cos A$
$tan A = sin A/cos A$
$sin^2 A + cos^2 A = 1$

$sec x + tan x = (1+sin x)/cos x = ((1+sin x)(1-sin x))/(cos x(1-sin x)) = (1-sin^2 x)/(cos x(1-sin x)) = cos x/(1-sin x)$

How do you verify cosx/(1-sinx)= secx+tanxcosx/(1-sinx)= secx+tanx?