If $\frac{x-xcosec^230°}{1+cosec^230°}= cos^260°=4cot^245°-sec^260°$, then the value of x is _________.
Answer & explanation
Correct answer: option 2
$\frac{x-xcosec^230°}{1+cosec^230°}= cos^260°=4cot^245°-sec^260°$
$\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 = - \(\frac{5}{ 4 × 3}\)
= - \(\frac{5}{ 12}\)