Given below are two statements:
Statement I: $$\dfrac{\cot 30^{o} + 1}{\cot 30^{o} - 1} = 2(\cos 30^{o} + 1)$$
Statement II: $$2 \sin 45^{o} \cos45^{o} - \tan 45^{o} \cot 45^{o} = 0$$

Statement I

$$\dfrac{\cot30+1}{\cot30-1}=\dfrac{\sqrt{3}+1}{\sqrt{3}-1}=\dfrac{\left(\sqrt{3}+1\right)^2}{\left(\sqrt{3}\right)^2-1^2}=2+\sqrt{3}$$

$$2\left(\cos30+1\right)=2\left(\dfrac{\sqrt{3}}{2}+1\right)=\sqrt{3}+2$$

Since both are equal, the statement I is true. 

Statement II

$$2\sin45\cos45-\tan45\cot45=2\left(\dfrac{1}{\sqrt{2}}\right)\left(\dfrac{1}{\sqrt{2}}\right)-1\times1=1-1=0$$

Statement II is true.