Question 1128175
 

prove {{{1/(1+cos(x))+1/(1-cos(x))=2csc(x)^2 }}}


start with left side

{{{1/(1+cos(x))+1/(1-cos(x)) }}}


{{{(1-cos(x))/((1-cos(x))(1+cos(x)))+(1+cos(x))/((1+cos(x))(1-cos(x)))}}}


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


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


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


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


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


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


={{{2/(1/csc^2(x))}}}


={{{2csc^2(x)}}}