Consider the following statements.I. sin ^{-1 | vedclass

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(B) Let $f(y) = y^2-4y+6 = (y-2)^2+2$. Since $(y-2)^2 \geq 0$,we have $f(y) \geq 2$ for all $y \in R$.For statement $I$: The identity $\sin^{-1}(x) +

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Only $II$

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(B) Let $f(y) = y^2-4y+6 = (y-2)^2+2$. Since $(y-2)^2 \geq 0$,we have $f(y) \geq 2$ for all $y \in R$.For statement $I$: The identity $\sin^{-1}(x) + \cos^{-1}(x) = \frac{\pi}{2}$ holds if and only if $x \in [-1, 1]$. Here,$f(y) \geq 2$,so $f(y)$ is never in $[-1, 1]$. Thus,statement $I$ is false.For statement $II$: The identity $\sec^{-1}(x) + \operatorname{cosec}^{-1}(x) = \frac{\pi}{2}$ holds if and only if $|x| \geq 1$. Since $f(y) \geq 2$,the condition $|f(y)| \geq 1$ is satisfied for all $y \in R$. Thus,statement $II$ is true.

Consider the following statements.
$I$. $\sin ^{-1}(y^2-4y+6)+\cos ^{-1}(y^2-4y+6) = \frac{\pi}{2}, \forall y \in R$
$II$. $\sec ^{-1}(y^2-4y+6)+\operatorname{cosec}^{-1}(y^2-4y+6) = \frac{\pi}{2}, \forall y \in R$
Which of the above statement$(s)$ is/are true?

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Consider the following statements.$I$. $\sin ^{-1}(y^2-4y+6)+\cos ^{-1}(y^2-4y+6) = \frac{\pi}{2}, \forall y \in R$$II$. $\sec ^{-1}(y^2-4y+6)+\operatorname{cosec}^{-1}(y^2-4y+6) = \frac{\pi}{2}, \forall y \in R$Which of the above statement$(s)$ is/are true?