COMEDK · Maths · 23. Inverse Trigonometric Functions
The solution of \(\tan ^{-1} x+2 \cot ^{-1} x=\frac{2 \pi}{3}\) is
- A \(\frac{1}{\sqrt{3}}\)
- B \(-\frac{1}{\sqrt{3}}\)
- C \(\sqrt{3}\)
- D \(-\sqrt{3}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{3}\)
Step-by-step Solution
Detailed explanation
We have, \(\Rightarrow \tan ^{-1} x+\cot ^{-1} x+\cot ^{-1} x=\frac{2 \pi}{3}\) \(\Rightarrow \quad \frac{\pi}{2}+\cot ^{-1} x=\frac{2 \pi}{3}\) \(\Rightarrow \quad \cot ^{-1} x=\frac{2 \pi}{3}\) \(\Rightarrow \quad \cot ^{-1} x=\frac{\pi}{6}\)…
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