Question 1154792

{{{(csc(x)*cos(x))/(csc(x)-sin(x))=sec(x)}}}

manipulate left side

{{{(csc(x)*cos(x))/(csc(x)-sin(x))}}} .......use identity:  {{{cos(x)=1/sec(x)}}} and {{{sin(x)=1/csc(x)}}}


={{{(csc(x)*(1/sec(x) ))/(csc(x)-1/csc(x)) }}}


={{{(csc(x)/sec(x) )/((csc^2(x)-1)/csc(x))}}} .........{{{(csc^2(x)-1)=cot^2(x)}}}


={{{(csc(x)/sec(x) )/(cot^2(x)/csc(x)) }}}


= {{{csc^2(x)/(sec(x)*cot^2(x))}}} .........{{{cot^2(x)=cos^2(x)/sin^2(x)=(1/sec^2(x))/(1/csc^2(x))=csc^2(x)/sec^2(x)}}}


= {{{cross(csc^2(x))1/(cross(sec(x))*(cross(csc^2 (x))/sec^cross(2)(x))) }}}


= {{{1/(1/sec(x)) }}}


= {{{sec(x)}}}