Discussion
What is the value of \(\tan 75° + \cot 75°\)?
Answer: C
First, find the values of \(\tan 75°\) and \(\cot 75°\).
\(\tan 75° = \tan(45°+30°) = \frac{\tan 45 + \tan 30}{1 - \tan 45 \tan 30} = \frac{1+1/\sqrt{3}}{1-1/\sqrt{3}} = \frac{\sqrt{3}+1}{\sqrt{3}-1} = 2+\sqrt{3}\).
\(\cot 75° = 1/\tan 75° = \frac{1}{2+\sqrt{3}} = 2-\sqrt{3}\).
The sum is \((2+\sqrt{3}) + (2-\sqrt{3}) = 4\).
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