Question 695154
{{{sin(x)/(1+cos(x))=(1-cos(x))/sin(x)}}}

Because you deal with fractions you need to exclude from domain (possible answers) those values that will give you denominators equal to zero.

{{{1+cos(x) =0}}}
{{{cos(x)=-1}}}
{{{x=pi}}}

{{{sin(x)=0}}}
{{{x=0}}} or {{{x=pi}}} or {{{x=2*pi}}}

So for the interval [{{{0}}},{{{2*pi}}}] we cannot have as solutions 0, {{{pi}}}, or {{{2*pi}}}.

Now as you do with any proportion, multiply on diagonal (butterfly method):

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

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

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

{{{1=1}}}

So this relation is true for every allowed value in the interval.