Question 1151359
manipulate left side:

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

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

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


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


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


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


={{{2(1+cos(x))/((1+cos(x))(sin(x))) }}} ...........simplify


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


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


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