jee-main 2025 Q20

jee-main · India · session1_24jan_shift2 Reciprocal Trig & Identities
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) $\pi$
(2) 0
(3) $\frac{\pi}{2} - (\alpha + \beta + \gamma)$
(4) $3\pi$
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) $\pi$\\
(2) 0\\
(3) $\frac{\pi}{2} - (\alpha + \beta + \gamma)$\\
(4) $3\pi$