If $\frac{x-xcosec^230°}{1+cosec^230°}= cos^260°=4cot^245°-sec^260°$, then the value of x is _________.

$-\frac{5}{12}$

$\frac{x-xcosec^230°}{1+cosec^230°}= cos^260°=4cot^245°-sec^260°$

  $\frac{x-x × 2²}{1+ 2²}= (\(\frac{1}{2}\) )² + 4 × 1 - 2² $

  $\frac{x - 4x }{5}= \(\frac{1}{4}\)  + 4  - 4 $

$\frac{-3x }{5}= \(\frac{1}{4}\)   $

x = - \(\frac{5}{ 4 × 3}\)

= - \(\frac{5}{ 12}\)