Question 1204326
 
1.


{{{(cos (theta +3pi/2) *csc(5pi + theta))/ (tan (theta -pi/2)* sin(-2theta))}}}

use

{{{cos (theta +3pi/2)=sin(theta)}}}

{{{csc(5pi + theta)=-csc(theta)}}}

{{{tan(theta ) *(-csc(2 theta ))=-cot(theta)}}}

 {{{sin(-2theta)= -sin(2theta)}}}



{{{(sin(theta)*(-csc(theta)))/(-cot(theta)*(-sin(2theta)))}}}



since

{{{sin(theta)*(-csc(theta))=-1}}}


then we have


{{{1/(-cot(theta)*(-sin(2theta)))}}}


{{{-1/(sin(2theta)* cot(theta))}}}


{{{-(1/sin(2theta))*(1/ cot(theta))}}}


{{{-(csc(2theta)*tan(theta) )}}}


{{{-csc(2theta)*tan(theta) }}}


2.

{{{(tan(theta -pi/2) *sin(-2theta))}}}

since:

{{{tan (theta-pi/2)=-cot(theta)}}}
{{{sin(-2theta)= -sin(2theta)}}}


then we have

{{{-cot(theta) *(-sin(2theta))}}}

{{{cot(theta) *sin(2theta)}}}