Question 743475
{{{(1+sin(x))^2/cos^2(x) = (1 + sin(x))/ (1-sin(x))}}}

For convenience we'll denote sin(x) as sinx. First we expand the numerator and rewrite the denominator:

{{{(1+sinx)^2/cos^2(x) = ((1 + sinx)(1 + sinx))/ (1^2-sin^2(x))}}}

Using the difference of squares identity for the denominator...

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

after cancelling...

{{{((1 + sinx)(1 + sinx))/((1 + sinx)(1 - sinx))=(1 + sinx)/(1 - sinx)}}}