<PRE><B>Question 952172</B>
{{{sec( theta)/(csc( theta)- cot( theta) )-sec ( theta)/(csc( theta)+cot ( theta))=2 csc ( theta)}}}


{{{((sec( theta)(csc( theta)+cot ( theta)))-(sec ( theta)(csc( theta)- cot( theta) )))/((csc( theta)- cot( theta) )(csc( theta)+cot ( theta)))=2 csc ( theta)}}}


{{{((sec( theta)csc( theta)+cot ( theta)sec( theta))-(sec ( theta)csc( theta)- cot( theta) sec ( theta)))/((csc^2( theta)- cot^2( theta) ))=2 csc ( theta)}}}



{{{((2 csc(2 theta)+csc(theta))-(2 csc(2 theta)- csc(theta)))/((csc^2( theta)- cot^2( theta)) )=2 csc ( theta)}}}

 =&gt;since {{{csc^2( theta)- cot^2( theta) =1}}}, we have

{{{((2 csc(2 theta)+csc(theta))-2 csc(2 theta)+ csc(theta)))/((csc^2( theta)- cot^2( theta) ))=2 csc ( theta)}}}


{{{((cross(2 csc(2 theta))+2csc(theta))-cross(2 csc(2 theta))))/1=2 csc ( theta)}}}

{{{2csc(theta)=2csc( theta)}}}

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