Inverse Trigonometric Functions PYQs - Last 5 Years
TS EAMCET / Mathematics / Trigonometry / 28 recent questions
MathematicsTrigonometry2021-2025
Practice 28 TS EAMCET Mathematics questions from Inverse Trigonometric Functions. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2024-2025
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Last 5 Years Inverse Trigonometric Functions Questions
Showing 28 of 28 filtered questions.
1Inverse Trigonometric Functions
\(\sin ^{-1}(-\cos 2)+\cos ^{-1}(\sin 3)+\tan ^{-1}(\cot 5)=\)
MCQ+1 / -02025
2Inverse Trigonometric Functions
The domain of the derivative of the function $f(x)=\cos ^{-1}(2 x-5)-\sin ^{-1}(x-2)$ is
MCQ+1 / -02025
3Inverse Trigonometric Functions
The number of real solution of $\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}$ is
MCQ+1 / -02025
4Inverse Trigonometric Functions
Consider the following
Assertion
$$ \begin{aligned} & \text { (A) } \begin{array}{r} \sqrt{x-3}\left(\sin ^{-1}(\log x)+\cos ^{-1}\right. \\ (\log x) d x=\frac{\pi}{3}(x-3)^{3 / 2}+c \end{array} \end{aligned} $$
Reason $(\mathrm{R}) \sin ^{...
Assertion
$$ \begin{aligned} & \text { (A) } \begin{array}{r} \sqrt{x-3}\left(\sin ^{-1}(\log x)+\cos ^{-1}\right. \\ (\log x) d x=\frac{\pi}{3}(x-3)^{3 / 2}+c \end{array} \end{aligned} $$
Reason $(\mathrm{R}) \sin ^{...
MCQ+1 / -02025
5Inverse Trigonometric Functions
If $\sinh ^{-1} x=\cosh ^{-1} y=\log (1+\sqrt{2})$, then $\tan ^{-1}(x+y)$
MCQ+1 / -02025
6Inverse Trigonometric Functions
If $0 \leq x<\frac{3}{4}$, then the number of values of $x$ satisfying the equation $\tan ^{-1}(2 x-1)+\tan ^{-1} 2 x= \tan ^{-1} 4 x-\tan ^{-1}(2 x+1)$ is
MCQ+1 / -02025
7Inverse Trigonometric Functions
If $y=\sec ^{-1} x$, then $\frac{d^2 y}{d x^2}=$
MCQ+1 / -02025
8Inverse Trigonometric Functions
The number of values of $x$ satisfying the equation, $\tan ^{-1}\left(x+\frac{\sqrt{2}}{x}\right)+\tan ^{-1}\left(x-\frac{\sqrt{2}}{x}\right)=\tan ^{-1}(x)$ is
MCQ+1 / -02025
9Inverse Trigonometric Functions
If $f(x)=\sqrt{\cos ^{-1} \sqrt{1-x^2}}$, then $f^{\prime}\left(\frac{1}{2}\right)=$
MCQ+1 / -02025
10Inverse Trigonometric Functions
If $2 \tanh ^{-1} x=\sinh ^{-1}\left(\frac{4}{3}\right)$, then $\cosh ^{-1}\left(\frac{1}{x}\right)=$
MCQ+1 / -02025
11Inverse Trigonometric Functions
\(\tan ^{-1} \frac{3}{5}+\tan ^{-1} \frac{6}{41}+\tan ^{-1} \frac{9}{191}=\)
MCQ+1 / -02025
12Inverse Trigonometric Functions
The range of the real value function $f(x)=\sin ^{-1}\left(\sqrt{x^2+x+1}\right)$ is
MCQ+1 / -02025
13Inverse Trigonometric Functions
Consider the following statements
Assertion (A) For $x \in R-\{1\}$;
\(\frac{d}{d x}\left(\tan ^{-1}\left(\frac{1+x}{1-x}\right)\right)=\frac{d}{d x}\left(\tan ^{-1} x\right)\)
Reason (R) For $x<1, \tan ^{-1}\left(\frac{1+x}{1-x}\right)=\...
Assertion (A) For $x \in R-\{1\}$;
\(\frac{d}{d x}\left(\tan ^{-1}\left(\frac{1+x}{1-x}\right)\right)=\frac{d}{d x}\left(\tan ^{-1} x\right)\)
Reason (R) For $x<1, \tan ^{-1}\left(\frac{1+x}{1-x}\right)=\...
MCQ+1 / -02025
14Inverse Trigonometric Functions
If $y=\left(\sin ^{-1} x\right)^2$, then $\left(1-x^2\right) \frac{d^2 y}{d x^2}-x \frac{d y}{d x}=$
MCQ+1 / -02025
15Inverse Trigonometric Functions
If $e^{\left(\sinh ^{-1} 2+\cosh ^{-1} \sqrt{6}\right)}=(a+(b+\sqrt{c}) \sqrt{a}+b \sqrt{c})$, then $a+b+c=$
MCQ+1 / -02025
16Inverse Trigonometric Functions
Consider the following statements
Assertion (A) : When $x, y, z$ are positive numbers, then
$$ \begin{aligned} & \tan ^{-1}\left(\sqrt{\frac{x(x+y+z)}{y z}}\right)+\tan ^{-1}\left(\sqrt{\frac{y(x+y+z)}{x z}}\right) +\tan ^{-1}\left(\sqrt{\f...
Assertion (A) : When $x, y, z$ are positive numbers, then
$$ \begin{aligned} & \tan ^{-1}\left(\sqrt{\frac{x(x+y+z)}{y z}}\right)+\tan ^{-1}\left(\sqrt{\frac{y(x+y+z)}{x z}}\right) +\tan ^{-1}\left(\sqrt{\f...
MCQ+1 / -02025
17Inverse Trigonometric Functions
$\cos ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\tan ^{-1} \frac{16}{63}=$
MCQ+1 / -02024
18Inverse Trigonometric Functions
If $\cosh ^{-1}\left(\frac{5}{3}\right)+\sinh ^{-1}\left(\frac{3}{4}\right)=k$, then $e^k=$
MCQ+1 / -02024
19Inverse Trigonometric Functions
If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$
MCQ+1 / -02024
20Inverse Trigonometric Functions
Match the functions given in List I with their relevant characteristics from List II.
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MCQ+1 / -02024
21Inverse Trigonometric Functions
$\operatorname{sech}^{-1}\left(\frac{3}{5}\right)-\tanh ^{-1}\left(\frac{3}{5}\right)=$
MCQ+1 / -02024
22Inverse Trigonometric Functions
If $\sin ^{-1} x-\cos ^{-1} 2 x=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$, then $\tan ^{-1} x+\tan ^{-1}\left(\frac{x}{x+1}\right)=$
MCQ+1 / -02024
23Inverse Trigonometric Functions
If $\sin h^{-1}(-\sqrt{3})+\cos ^{-1}(2)=K$, then $\cosh K=$
MCQ+1 / -02024
24Inverse Trigonometric Functions
If $y=\cos ^{-1}\left(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}\right)$, then $\frac{d y}{d x}=$
MCQ+1 / -02024
25Inverse Trigonometric Functions
If the real valued function $f(x)=\sin ^{-1}\left(x^2-1\right)-3 \log _3\left(3^x-2\right)$ is not defined for all $x \in(-\infty, a) \cup(b, \infty)$, then $3^a+b^2=$
MCQ+1 / -02024
26Inverse Trigonometric Functions
If $\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\pi}{6}$, then $x=$
MCQ+1 / -02024
27Inverse Trigonometric Functions
The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$, has a solution
MCQ+1 / -02024
28Inverse Trigonometric Functions
The domain of the real valued function $f(x)=\sin ^{-1}\left(\log _{2}\left(\frac{x^{2}}{2}\right)\right)$ is
MCQ+1 / -02024