Question 1152016
sec (x) - cos( x) = sin( x) tan( x)


manipulate left side:

{{{sec (x) - cos( x)}}} ...................use identity {{{sec (x) =1/cos(x)}}}

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

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

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

={{{sin^2( x)/cos(x)}}}......write {{{sin^2( x)}}} as {{{sin( x)*sin( x)}}}

={{{( sin( x)*highlight(sin( x)))/highlight(cos(x))}}}.......use identity {{{sin(x)/cos(x)=tan(x)}}}

={{{ sin( x)*tan( x)}}}