Answer
$$\lim_{\theta\to0}\sin\theta\cot2\theta=\frac{1}{2}$$
Work Step by Step
$$A=\lim_{\theta\to0}\sin\theta\cot2\theta$$
$$A=\lim_{\theta\to0}\Big(\sin\theta\times\frac{\cos2\theta}{\sin2\theta}\Big)$$
$$A=\lim_{\theta\to0}\frac{\sin\theta\cos2\theta}{2\sin\theta\cos\theta}$$
$$A=\lim_{\theta\to0}\frac{\cos2\theta}{2\cos\theta}$$
$$A=\frac{\cos0}{2\cos0}$$
$$A=\frac{1}{2\times1}=\frac{1}{2}$$
