If $csc(x)=4,$ for $sin(\frac{x}{2})=$Prove the following identity: $\frac{1+cos(2x)}{sin(2x)}=\frac{1}{tan(x)}$

$\frac{1+cos(2x)}{sin(2x)}=$

${?}_{{?}_{?}}|=$

$cos(\frac{x}{2})=$

$tan(\frac{x}{2})=90,$ then

$sin(\frac{x}{2})=$

$cos(\frac{x}{2})=$

$tan(\frac{x}{2})=$