Question 1153470
manipulate left side

{{{-1/csc(-theta) - (cot(-theta)/sec(-theta))}}}.........since {{{csc(-theta) =-csc(theta)}}},{{{cot(-theta)=-cot(theta)}}}, and {{{sec(-theta)=sec(theta)}}}....common denominator is {{{-csc(theta)sec(theta)}}},


={{{-1/(-csc(theta)) - (-cot(theta)/sec(theta))}}}


={{{1/csc(theta)+cot(theta)/sec(theta)}}}


={{{sec(theta)/(sec(theta)csc(theta))+(cot(theta)csc(theta))/(csc(theta)sec(theta))}}}


={{{(sec(theta)+cot(theta)csc(theta))/(csc(theta)sec(theta))}}}


express all with {{{sin(theta) }}}and {{{cos(theta)}}}:

{{{sec(theta)=1/cos(theta)}}}
{{{csc(theta)=1/sin(theta) }}}
{{{cot(theta)=cos(theta)/sin(theta) }}}



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


={{{(1/cos(theta)+cos(theta)/sin^2(theta))/(1/(sin(theta)*cos(theta)))}}}


={{{(sin^2(theta)/(sin^2(theta)cos(theta))+cos^2(theta)/(cos(theta)sin^2(theta)))/(1/(sin(theta)*cos(theta)))}}}


={{{((sin^2(theta)+cos^2(theta))/(cos(theta)sin^2(theta)))/(1/(sin(theta)*cos(theta)))}}}....{{{sin^2(theta)+cos^2(theta)=1}}}


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


={{{(sin(theta)*cos(theta))/(cos(theta)*sin^2(theta))}}}...simplify


={{{(cross(sin(theta))*cross(cos(theta))1)/(cross(cos(theta))*sin^cross(2)(theta))}}}


={{{1/sin(theta)}}}........use identity {{{csc(theta)=1/sin(theta) }}}


={{{csc(theta)}}}