Trigonometric Limits

Find:$ \mathop{\lim}\limits_{n \to \frac{\pi}{2}}\frac{cotx-cosx}{(\pi-2x)^3} $
You have to take

$$y=\frac{\pi}{2}-x$$
$$\cot x=\cot (\frac{\pi}{2}-y)=\tan y$$
$$\cos x=\cos (\frac{\pi}{2}-y)=\sin y$$
$$\lim_{y \to 0}\frac{\tan y-\sin y}{8y^3}=\frac{1}{8}\lim_{y \to 0}\frac{\tan y}{y}\lim_{y \to 0}\frac{1-\cos y}{y^2}=\frac{1}{16}$$

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