Question:
If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?
If \(|x|\ge1\), then \(\tan\!\left[\dfrac{2}{3}\big(\tan^{-1}x+\cot^{-1}x\big)\right]=\) ?
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Once the inside is a fixed angle, evaluate the outer trig directly.
Updated On: Oct 17, 2025
- \(\dfrac{12}{\sqrt3}\)
- \(\sqrt3\)
- \(0\)
- \(1\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Using \(\tan^{-1}x+\cot^{-1}x=\dfrac{\pi}{2}\),
\[
\tan\!\left[\frac{2}{3}\cdot\frac{\pi}{2}\right]=\tan\!\left(\frac{\pi}{3}\right)=\sqrt3.
\]
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