What is the value of $$\cot 35^\circ \cot 40^\circ \cot 45^\circ \cot 50^\circ \cot 55^\circ$$ ?

$$\cot 35^\circ \cot 40^\circ \cot 45^\circ \cot 50^\circ \cot 55^\circ$$ = $$\cot35^{\circ}\cot40^{\circ}\cot45^{\circ}\cot\left(90-40\right)^{\circ}\cot\left(90-35\right)^{\circ}$$

= $$\cot35^{\circ}\cot40^{\circ}\cot45^{\circ}\tan40^{\circ}\tan35^{\circ}$$

= $$\left(\cot35^{\circ}\tan35^{\circ}\right)\left(\cot40^{\circ}\tan40^{\circ}\right)\cot45^{\circ}$$

= $$\left(1\right)\left(1\right)\left(1\right)$$

= $$1$$

Hence, the correct answer is Option C