The value of _ x → 0 ((x)/(1 - x8 - 1 + x8)) is equal to :

$\lim_{x \to 0}\left(\dfrac{x}{1 - \sin x8 - 1 + \sin x8}\right)$

$= \lim_{x \to 0}\left(\dfrac{x}{1 - \sin x8 - 1 + \sin x8}\right) \times$$\left(\dfrac{1 - \sin x8 + 1 + \sin x8}{1 - \sin x8 + 1 + \sin x8}\right) \times$

\left(\dfrac{1 - \sin x4 + 1 + \sin x4}{1 - \sin x4 + 1 + \sin x4}\right) \times$</p><p>\left(\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}\right)$

$= \lim_{x \to 0}\left(\dfrac{x}{1 - \sin x - ( 1 + \sin x )}\right) \times$

\left(1 - \sin x8 + 1 + \sin x8\right)\left(1 - \sin x4 + 1 + \sin x4\right)\left(\sqrt{1 - \sin x} + \sqrt{1 + \sin x}\right)$</p><p>$= \lim_{x \to 0}\dfrac{x}{( - 2\sin x )}\left(1 - \sin x8 + 1 + \sin x8\right) \times$</p><p>\left(1 - \sin x4 + 1 + \sin x4\right)\left(\sqrt{1 - \sin x} + \sqrt{1 + \sin x}\right)$

$=\lim_{x \to 0}\left(- \dfrac{1}{2}\right)\left(2\right)\left(2\right)\left(2\right)\left\{∵ \lim_{x \to 0}\dfrac{\sin x}{x} = 1\right\} = - 4$