<PRE><B>Question 1127996</B>
{{{csc^2(theta)/(csc^2(theta)+sec^2(theta) )}}}

use: 

{{{csc^2(theta)=1/sin^2(theta)}}}

{{{sec^2(theta) =1/cos^2(theta)}}}


={{{(1/sin^2(theta))/(1/sin^2(theta)+1/cos^2(theta) )}}}


={{{(1/sin^2(theta))/((cos^2(theta)+sin^2(theta))/(sin^2(theta)*cos^2(theta) ))}}}



={{{(1/sin^2(theta))/(1/(sin^2(theta)*cos^2(theta) ))}}}



={{{(1/cross(sin^2(theta)))/(1/(cross(sin^2(theta))*cos^2(theta) ))}}}



={{{(1/1)/(1/cos^2(theta) )}}}


={{{cos^2(theta)}}}

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