Question 1040632

Prove that:

Cosx/1-sinx + 1-sinx/cosx = 2secx
<pre>{{{cos (x)/(1 - sin (x)) + (1 - sin (x))/cos (x) = 2 * sec (x)}}}
{{{(cos (x) * cos (x) + (1 - sin (x))(1 - sin (x)))/(1 - sin (x)(cos (x)))}}} ------- Multiplying left-side by LCD, (1 - sin x)(cos x)
{{{(cos^2 (x) + (1 - 2sin (x) + sin^2 (x)))/(1 - sin (x)(cos (x)))}}} 
{{{(cos^2 (x) + 1 - 2sin (x) + sin^2 (x))/(1 - sin (x)(cos (x)))}}} 
{{{(cos^2 (x) + sin^2 (x) - 2sin (x) + 1)/(1 - sin (x)(cos (x)))}}} 
{{{(1 - 2sin (x) + 1)/(1 - sin (x)(cos (x)))}}} ----- Substituting 1 for {{{cos^2 (x) + sin^2 (x)}}}
{{{(2 - 2sin (x))/(1 - sin (x)(cos (x)))}}} 
{{{2(1 - sin (x))/(1 - sin (x)(cos (x)))}}}_____{{{2cross((1 - sin (x)))/cross(1 - sin (x))cos (x)}}}_______{{{2 * (1/cos (x))}}} = {{{highlight_green(2 * sec (x))}}} (Same as right side)