Question 928224

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


start with left side:

{{{sin(x)/(1-sin(x))-sin (x)/(1+sin(x))}}}=


{{{(sin(x)(1+sin(x))-sin (x)(1-sin(x)))/((1-sin(x))(1+sin(x)))}}}=


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


{{{(2sin^2(x))/(1-sin^2(x))}}}=...use identity {{{1-sin^2(x)=cos^2(x)}}}


{{{2(sin^2(x)/cos^2(x))}}}=


{{{2tan^2(x)}}}