Help to solve this trigonometric problem.

{cos(x)-1+sin(x)}/{cos(x)+1-sin(x)} =
{cos(x)-1+sin(x)}/{cos(x)+1-sin(x)}* {cos(x)+1+sin(x)}/{cos(x)+1+sin(x)}=
{cos(x)-1+sin(x)}{cos(x)+1+sin(x)}/[{cos(x)+1-sin(x)}{cos(x)+1+sin(x)}]=
{cos(x)+sin(x)-1}{cos(x)+sin(x)+1}/[{cos(x)+1}^2-sin^2(x)}]=
{[cos(x)+sin(x)]^2-1}/{cos^2(x)+2cos(x)+1-sin^2(x)}=
{cos^2(x)+2cos(x)sin(x)+sin^2(x)-1}/{cos^2(x)+2cos(x)+cos^2(x)+sin^2(x)-sin^2(x)}=
{2cos(x)sin(x)}/{2cos^2(x)+2cos(x)}=
2cos(x)sin(x)/[2cos(x){cos(x)+1}=
sin(x)/{cos(x)+1}

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