Trigonometric Identities Question 5

Question: $ \tan A+\cot (180{}^\circ +A)+\cot (90{}^\circ +A)+\cot (360{}^\circ -A) $

[MP PET 1992]

Options:

A) 0

B) $ 2\tan A $

C) $ 2\cot A $

D) $ 2(\tan A-\cot A) $

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Answer:

Correct Answer: A

Solution:

$ \tan A+\cot (180{}^\circ +A)+\cot (90{}^\circ +A)+\cot (360{}^\circ -A) $ $ =\tan A+\cot A-\tan A-\cot A=0 $ .