Find the value of $$\tan35^{\circ}\cot40^{\circ}\tan45^{\circ}\cot50^{\circ}\tan55^{\circ}$$.
$$\tan35^{\circ}\cot40^{\circ}\tan45^{\circ}\cot50^{\circ}\tan55^{\circ}=\tan35^{\circ}\cot40^{\circ}\tan45^{\circ}\cot\left(90-40^{\circ}\right)\tan\left(90-35^{\circ}\right)$$
$$=\tan35^{\circ}\cot40^{\circ}\left(1\right)\tan40^{\circ}\cot35^{\circ}$$
$$=1$$
Hence, the correct answer is Option D
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