Trigonometric Identities Question 362

Question: $ \tan 75{}^\circ -\cot 75{}^\circ = $

[MNR 1982; Pb. CET 1990, 2000]

Options:

A) $ 2\sqrt{3} $

B) $ 2+\sqrt{3} $

C) $ 2-\sqrt{3} $

D) None of these

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Answer:

Correct Answer: A

Solution:

$ \tan ,75^{o}-\cot ,75^{o}=\cot ,15^{o}-\cot ,75^{o} $ $ =(2+\sqrt{3})-(2-\sqrt{3})=2\sqrt{3} $ .