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GUJCET · Maths · Inverse Trigonometric Functions
\(\cos ^{-1}\left\{\cot \left(\sum_{i=1}^3 \cot ^{-1} i\right)\right\}=\) ____________ .
- A \(-\frac{\pi}{2}\)
- B 0
- C \(\pi\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(\sum_{i=1}^3 \cot ^{-1} i = \cot ^{-1} 1 + \cot ^{-1} 2 + \cot ^{-1} 3\) \(= \tan ^{-1} 1 + \tan ^{-1} (1/2) + \tan ^{-1} (1/3)\)
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