AP EAPCET 2025 - 24th May Morning Shift | Inverse Trigonometric Functions Question 9 | Mathematics

If $A=\left\{x \in R / \sin ^{-1}\left(\sqrt{x^2+x+1}\right) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right\}$ and $B=\left\{y \in R / y=\sin ^{-1}\left(\sqrt{x^2+x+1}\right), x \in A\right\}$, then

$A \cap B \neq \phi$

$A \cap B^C=[0,1]$

$A^C \cap B=\left[\frac{\pi}{3}, \frac{\pi}{2}\right]$

$A \cup B=R-\left\{[-1,0] \cup\left[\frac{\pi}{3}, \frac{\pi}{2}\right]\right\}$

AP EAPCET 2025 - 24th May Morning Shift

MCQ (Single Correct Answer)

-0

The domain of the function, $f(x)=\sqrt{\log _e\left(\frac{1}{x^2-4 x+4}\right)}+\sin ^{-1}\left(x^2-2\right)$ is

$[1,3]$

$[1,3)$

$[1, \sqrt{3}]$

$[1, \sqrt{3})$

AP EAPCET 2025 - 24th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\frac{a}{\sqrt{b^2-a^2}}\right)\right\}, b>a$ then $x=$

$\frac{b}{\sqrt{2 b^2-a^2}}$

$\frac{a}{\sqrt{2 b^2-a^2}}$

$\frac{\sqrt{b^2-a^2}}{a}$

$\frac{\sqrt{b^2-a^2}}{b}$

AP EAPCET 2025 - 24th May Morning Shift

MCQ (Single Correct Answer)

-0

If $\sinh ^{-1} x=\log 3$ and $\cosh ^{-1} y=\log \frac{3}{2}$, then $\tanh ^{-1}(x-y)=$

$\log \sqrt{\frac{5}{3}}$

$\log \frac{5}{3}$

$\log \frac{4}{3}$

$\log \frac{2}{\sqrt{3}}$

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