Question:
For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).
For \(x\in\mathbb{R}\), compute \(\csc\!\big(\tan^{-1}x+\cot^{-1}x\big)\).
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Remember $\arctan x+\operatorname{arccot}x=\dfrac{\pi}{2}$ (principal values).
Updated On: Oct 17, 2025
- \(0\)
- \(1\)
- \(\dfrac{2}{\sqrt3}\)
- \(2\)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
With the standard principal ranges used in school exams,
\(\tan^{-1}x+\cot^{-1}x=\dfrac{\pi}{2}\).
Therefore
\[
\csc\!\left(\tan^{-1}x+\cot^{-1}x\right)=\csc\!\left(\frac{\pi}{2}\right)=1.
\]
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