JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The principal value of \({\tan ^{ - 1}}\left( {\cot \frac{{43\pi }}{4}} \right)\) is
- A \(-\frac{3\pi}{4}\)
- B \(\frac{3\pi}{4}\)
- C \(-\frac{\pi}{4}\)
- D \(\frac{\pi}{4}\)
Answer & Solution
Correct Answer
(C) \(-\frac{\pi}{4}\)
Step-by-step Solution
Detailed explanation
Consider \({\tan ^{ - 1}}\left[ {\cot \frac{{43\pi }}{4}} \right]\) \( = {\tan ^{ - 1}}\left[ {\cot \left( {10\pi + \frac{{43\pi }}{4}} \right)} \right]\) \( = {\tan ^{ - 1}}\left[ {\cot \frac{{3\pi }}{4}} \right]\) [\(\because \)…
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