Question 1140548
 {{{(csc^4(x)-1)/(cot^2(x))=2+cot^2(x) }}}

manipulating left side

 ={{{(csc^4(x)-1)/(cot^2(x))}}}.......use identity {{{cot^2(x)= csc^2(x)-1}}}

 ={{{(csc^4(x)-1)/(csc^2(x)-1)}}}.......factor numerator : {{{ (csc^4(x)-1)= ((csc^2(x))^2-1)= (csc^2(x)-1) (csc^2(x)+1)}}}

 ={{{( (csc^2(x)-1) (csc^2(x)+1))/(csc^2(x)-1)}}}......simplify

 ={{{( cross((csc^2(x)-1)) (csc^2(x)+1))/(cross(csc^2(x)-1))}}}

={{{csc^2(x)+1}}}................use the following identity : {{{csc ^2 (x )=1+ cot ^2 (x )}}}

={{{1+ cot ^2 (x )+1}}}

={{{2+ cot ^2 (x )}}}