Question 405196
Let work with left side {{{sin(x)*(tan(x)cos(x)-cot(x)cos(x))}}}
Use formulas {{{tan (x)=sin(x)/cos(x)}}}, {{{cot(x)=cos(x)/sin(x)}}}
{{{sin(x)*(tan(x)cos(x)-cot(x)cos(x))=sin(x)*((sin(x)/cross(cos(x)))(cross(cos(x)))-(cos(x)/sin(x))cos(x))=sin(x)*sin(x)-cross(sin(x))*(cos(x)^2)/(cross(sin(x)))=(sin(x))^2-(cos(x))^2}}}
use formula {{{(sin(x))^2=1-(cos(x))^2}}}
{{{(sin(x))^2-(cos(x))^2=1-(cos(x))^2-(cos(x))^2=1-2(cos(x))^2}}}