Question 1207012
{{{cos^2(x)=(csc(x)cos(x))/(tan(x)+cot(x))}}}


manipulate right side

{{{(csc(x)cos(x))/(tan(x)+cot(x))}}}.....use identities: {{{csc(x)=1/sin(x)}}}, {{{tan(x)=sin(x)/cos(x)}}}, {{{cot(x)=cos(x)/sin(x)}}}


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


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


={{{(cos(x)/sin(x))/(1/(sin(x)*cos(x)))}}}...simplify


={{{(cos(x)/cross(sin(x))1)/(1/(cross(sin(x))1*cos(x)))}}}


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


={{{cos(x)*cos(x)}}}


={{{cos^2(x)}}}=> proven