Question 175830
Remember, {{{tan(x)=sin(x)/cos(x)}}}. So {{{sin(x)/tan(x)=sin(x)/(sin(x)/cos(x))=cross(sin(x))(cos(x)/cross(sin(x)))=cos(x)}}}. In other words, {{{sin(x)/tan(x)=cos(x)}}}



So {{{sec(x)(sin(x)/tan(x))-1}}} becomes {{{sec(x)cos(x)-1}}}



Now replace sec(x) with {{{1/cos(x)}}} to get {{{(1/cos(x))cos(x)-1}}}



Multiply to get {{{1-1}}} and subtract to get {{{0}}}



So {{{sec(x)(sin(x)/tan(x))-1=0}}}