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Jee Main 2025 — Medium JEE math MCQ

If $\alpha > \beta > \gamma > 0$, then the expression $\cot^{-1} \left\{ \beta + \frac{(1+\beta^2)}{(\alpha-\beta)} \right\} + \cot^{-1} \left\{ \gamma + \frac{(1+\gamma^2)}{(\beta-\gamma)} \right\} + \cot^{-1} \left\{ \alpha + \frac{(1+\alpha^2)}{(\gamma-\alpha)} \right\}$ is equal to
  1. A. $\pi$
  2. B. 0
  3. C. $\pi - (\alpha + \beta + \gamma)$
  4. D. $3\pi$

Solution

The correct option is **A**. (A. $\pi$)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
If α>β>γ>0\alpha > \beta > \gamma > 0, then the expression cot⁡−1{β+(1+β2)(α−β)}+cot⁡−1{γ+(1+γ2)(β−γ)}+cot⁡−1{α+(1+α2)(γ−α)}\cot^{-1} \left\{ \beta + \frac{(1+\beta^2)}{(\alpha-\beta)} \right\} + \cot^{-1} \left\{ \gamma + \frac{(1+\gamma^2)}{(\beta-\gamma)} \right\} + \cot^{-1} \left\{ \alpha + \frac{(1+\alpha^2)}{(\gamma-\alpha)} \right\} is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep