Question 1206215
{{{cot(x) - tan(x) = sec(x)(csc(x) - 2 sin(x))}}}

left side

{{{cot(x) - tan(x)}}}....use identity {{{cot(x)=cos(x)/sin(x) }}}and {{{tan(x)=sin(x)/cos(x)}}}


={{{cos(x)/sin(x)-sin(x)/cos(x)}}}


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


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


={{{(1-2sin^2(x))/(sin(x)*cos(x))}}}...expand


={{{1/(sin(x)*cos(x))-(2sin^2(x))/(sin(x)*cos(x))}}}...simplify


={{{(1/sin(x))*(1/cos(x))-2sin(x)(1/cos(x))}}}...use identity {{{1/sin(x)=csc(x) }}}and {{{1/cos(x)=sec(x)}}}




={{{csc(x) *sec(x)-(2sin(x))(sec(x))}}}...factor out{{{ sec(x)}}}


={{{sec(x)(csc(x) -2sin(x))}}}