Inverse Trigonometric Functions · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1

If $0 < x < \frac{1}{2}$ and $\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)$, then $\tan \alpha+\cot \alpha$ is equal to

AP EAPCET 2024 - 23th May Morning Shift
2
$\cot \left(\sum\limits_{n=1}^{50} \tan ^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is equal to
AP EAPCET 2024 - 22th May Evening Shift
3
The value of $x$ such that $\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\cos \left(2 \tan ^{-1} x)\right.$
AP EAPCET 2024 - 22th May Morning Shift
4
The range of the real valued function $f(x)=\sin ^{-1}\left(\frac{1+x^2}{2 x}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)$ is
AP EAPCET 2024 - 21th May Evening Shift
5
The real values of $x$ that satisfy the equation $\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}$ is
AP EAPCET 2024 - 21th May Evening Shift
6
$2 \operatorname{coth}^{-1}(4)+\sec h^{-1}\left(\frac{3}{5}\right)=$
AP EAPCET 2024 - 21th May Evening Shift
7
If $y=\sin ^{-1} x$, then $\left(1-x^2\right) y_2-x y_1=$
AP EAPCET 2024 - 21th May Evening Shift
8
If $\cos ^{-1} 2 x+\cos ^{-1} 3 x=\frac{\pi}{3}$ and $4 x^2=\frac{a}{b}$, then $a+b$ is equal to
AP EAPCET 2024 - 20th May Evening Shift
9
If $\theta=\sec ^{-1}(\cosh u)$, then $u=$
AP EAPCET 2024 - 20th May Evening Shift
10
If $\cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}=k$, then $\sin ^{-1}\left(\sqrt{\frac{k}{2}}\right)+\cos ^{-1}\left(\frac{k}{3}\right)=$
AP EAPCET 2024 - 20th May Morning Shift
11
$$4 \tan ^{-1} \frac{1}{5}-\tan ^{-1} \frac{1}{70}+\tan ^{-1} \frac{1}{99}=$$
AP EAPCET 2024 - 20th May Morning Shift
12
$$ \cosh \left(\sinh ^{-1}(\sqrt{8})+\cosh ^{-1} 5\right)= $$
AP EAPCET 2024 - 19th May Evening Shift
13
$\tan^{-1} 2 + \tan^{-1} 3 = $
AP EAPCET 2024 - 18th May Morning Shift
14

If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$, then

AP EAPCET 2021 - 20th August Morning Shift
15

$$\frac{d}{d x}\left\{\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\right\}$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
16

If $$y=\tan ^{-1}\left\{\frac{a x-b}{b x+a}\right\}$$, then $$y^{\prime}$$ is equal to

AP EAPCET 2021 - 20th August Morning Shift
17

For how many distinct values of $$x$$, the following $$\sin \left[2 \cos ^{-1} \cot \left(2 \tan ^{-1} x\right)\right]=0$$ holds?

AP EAPCET 2021 - 19th August Evening Shift
18

If $$\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\frac{1}{1+n(1+1)}\right]=\tan ^{-1}[x]$$, then $$x$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
19

If $$y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)$$, where $$x^2 \leq 1$$. Then, find $$\frac{d y}{d x}$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
20

If $$\int \frac{d x}{x\left(\sqrt{\left.x^4-1\right)}\right.}=\frac{1}{k} \sec ^{-1}\left(x^k\right)$$, then the value of $$k$$ is equal to

AP EAPCET 2021 - 19th August Morning Shift
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