Question 1012067
 {{{ (sec (x)/ sin (x)) - (cos( x)/ sin (x)) }}} ............since {{{sec (x) =1/cos(x)}}}, we have


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


= {{{(1/(cos(x)sin (x))) - (cos( x)/ sin (x))}}}.....common denominator is {{{ cos(x)cos( x)}}}


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


={{{(1 - cos^2( x))/ (cos(x)sin (x))}}}............ since {{{1 - cos^2( x)=sin^2 (x)}}}, we have


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


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


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


={{{tan(x)}}}