jee-main 2024 Q71

jee-main · India · session1_31jan_shift1 Reciprocal Trig & Identities
For $\alpha , \beta , \gamma \neq 0$. If $\sin ^ { - 1 } \alpha + \sin ^ { - 1 } \beta + \sin ^ { - 1 } \gamma = \pi$ and $(\alpha + \beta + \gamma)(\alpha - \gamma + \beta) = 3 \alpha \beta$, then $\gamma$ equals
(1) $\frac { \sqrt { 3 } } { 2 }$
(2) $\frac { 1 } { \sqrt { 2 } }$
(3) $\frac { \sqrt { 3 } - 1 } { 2 \sqrt { 2 } }$
(4) $\sqrt { 3 }$
For $\alpha , \beta , \gamma \neq 0$. If $\sin ^ { - 1 } \alpha + \sin ^ { - 1 } \beta + \sin ^ { - 1 } \gamma = \pi$ and $(\alpha + \beta + \gamma)(\alpha - \gamma + \beta) = 3 \alpha \beta$, then $\gamma$ equals\\
(1) $\frac { \sqrt { 3 } } { 2 }$\\
(2) $\frac { 1 } { \sqrt { 2 } }$\\
(3) $\frac { \sqrt { 3 } - 1 } { 2 \sqrt { 2 } }$\\
(4) $\sqrt { 3 }$