WBJEE · Maths · Inverse Trigonometric Functions
The value of \(2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}\) is
- A \(-\frac{\pi}{8}\)
- B \(\frac{3 \pi}{2}\)
- C \(\frac{\pi}{4}\)
- D \(\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
\(2 \cot ^{-1} \frac{1}{2}-\cot ^{-1} \frac{4}{3}\) \(\begin{array}{l} =2 \tan ^{-1} 2-\tan ^{-1} \frac{3}{4} \\ =\pi+\tan ^{-1} \frac{4}{-3}-\tan ^{-1} \frac{3}{4} \\ =\pi-\tan ^{-1} \frac{4}{3}-\tan ^{-1} \frac{3}{4} \end{array}\)…
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