AP EAPCET 2025 - 26th May Evening Shift | Inverse Trigonometric Functions Question 8 | Mathematics

If $f(x)=\sec ^{-1}\left(\frac{1}{2 x^2-1}\right)$ and $g(x)=\tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$, then the derivative of $f(x)$ with respect to $g(x)$ is

$\frac{1+x^2}{4 \sqrt{1-x^2}}$

$\frac{\left(1-x^2\right)}{4 \sqrt{1+x^2}}$

$-\frac{4\left(1-x^2\right)}{\sqrt{1+x^2}}$

$-\frac{4\left(1+x^2\right)}{\sqrt{1-x^2}}$

AP EAPCET 2025 - 24th May Morning Shift

MCQ (Single Correct Answer)

-0

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 $x=$

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

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

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

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

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