Question 752542
{{{(sec(x)/sin(x)) - (sin(x)/cos(x)) = cot(x)}}}


{{{(sec(x))(1/(sin(x))) - (sin(x))/(cos(x)) = cot(x)}}}.....since {{{1/(sinx)=csc(x)}}} and {{{(sin(x))/(cos(x)) = tan(x)}}}, we will have


{{{sec(x)csc(x) - tan(x) = cotx}}}........since {{{sec(x) = 1 / cos(x)}}} => {{{cos(x) = 1 / sec(x)}}}, then {{{tan(x)=sec(x)sin(x)}}} 


{{{sec(x)csc(x) - sec(x)sin(x) = cot(x)}}}


{{{sec(x)(csc(x) - sin(x)) = cot(x)}}}


{{{sec(x)(csc(x) - sin(x)) = cot(x)}}}........since {{{csc(x) - sin(x)=cos(x)cot(x)}}}


{{{sec(x)cos(x)cot(x) = cot(x)}}}........again {{{sec(x) = 1 / cos(x)}}}


{{{(1 / cos(x))cos(x)cot(x) = cot(x)}}}


{{{(1 / cross(cos(x)))cross(cos(x))cot(x) = cot(x)}}}


{{{cot(x) = cot(x)}}}