jee-main 2024 Q72

jee-main · India · session2_04apr_shift2 Complex Numbers Arithmetic True/False or Property Verification Statements

Given that the inverse trigonometric function assumes principal values only. Let $x , y$ be any two real numbers in $[ - 1,1 ]$ such that $\cos ^ { - 1 } x - \sin ^ { - 1 } y = \alpha , \frac { - \pi } { 2 } \leq \alpha \leq \pi$. Then, the minimum value of $x ^ { 2 } + y ^ { 2 } + 2 x y \sin \alpha$ is
(1) 0
(2) - 1
(3) $\frac { 1 } { 2 }$
(4) $- \frac { 1 } { 2 }$

Given that the inverse trigonometric function assumes principal values only. Let $x , y$ be any two real numbers in $[ - 1,1 ]$ such that $\cos ^ { - 1 } x - \sin ^ { - 1 } y = \alpha , \frac { - \pi } { 2 } \leq \alpha \leq \pi$.\\
Then, the minimum value of $x ^ { 2 } + y ^ { 2 } + 2 x y \sin \alpha$ is\\
(1) 0\\
(2) - 1\\
(3) $\frac { 1 } { 2 }$\\
(4) $- \frac { 1 } { 2 }$

Paper Questions

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