List of top Mathematics Questions on Inverse Trigonometric Functions asked in JEE Main

If the domain of the function $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha)\cup[\beta,\gamma]\cup[\delta,\infty)$, then $\alpha+\beta+\gamma+\delta$ is equal to

The number of solutions of \[ \tan^{-1}(4x) + \tan^{-1}(6x) = \frac{\pi}{6}, \] where \[ -\frac{1}{2\sqrt{6}}<x<\frac{1}{2\sqrt{6}}, \] is equal to

Let the maximum value of $ (\sin^{-1}x)^2 + (\cos^{-1}x)^2 $ for $ x \in \left[ -\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}} \right] $ be $ \frac{m}{n}\pi^2 $, where $ \gcd(m, n) = 1 $. Then $ m + n $ is equal to _________.

If the domain of the function $f(x) = \cos^{-1}\left(\frac{2x-5}{11-3x}\right) + \sin^{-1}(2x^2-3x+1)$ is the interval $[\alpha, \beta]$, then $\alpha + 2\beta$ is equal to:}

If domain of $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha]\cup[\beta,\gamma]\cup[\delta,\infty)$, then $(\alpha+\beta+\gamma+\delta)$ is

If the domain of the function \[ \cos^{-1}\!\left(\frac{2x-5}{11x-7}\right) + \sin^{-1}\!\left(2x^2 - 3x + 1\right) \] is \[ [0,a] \cup \left[\frac{12}{13},\, b\right], \] then the value of $ \dfrac{1}{ab} $ is:

Let \[ k = \tan\!\left(\frac{\pi}{4} + \frac{1}{2}\cos^{-1}\!\frac{2}{3}\right) + \tan^{-1}\!\left(\frac{1}{2}\sin^{-1}\!\frac{2}{3}\right). \] Then the number of solutions of the equation \[ \sin^{-1}(kx - 1) = \sin^{-1}x - \cos^{-1}x \] is:

If domain of $f(x)=\sin^{-1}\!\left(\dfrac{1}{x^2-2x-2}\right)$ is $(-\infty,\alpha]\cup[\beta,\gamma]\cup[\delta,\infty)$, then $(\alpha+\beta+\gamma+\delta)$ is

The number of values of $x$ satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is

The value of $\int_{-1}^{1} \frac{(1 + \sqrt{|x| - x})e^x + (\sqrt{|x| - x})e^{-x}}{e^x + e^{-x}} \, dx$ is equal to

Considering the principal values of the inverse trigonometric functions, $\sin^{-1} \left( \frac{\sqrt{3}}{2} x + \frac{1}{2} \sqrt{1-x^2} \right)$, $-\frac{1}{2}<x<\frac{1}{\sqrt{2}}$, is equal to

\[ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20, \quad \alpha \text{ is one of the roots of } x^2 + x + 1 = 0, \text{ then } n = ? \]

\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of $16((sec^{-1}x)^{2}+(cosec^{-1}x)^{2})$ is:

Given the inverse trigonometric function assumes principal values only. Let $ x, y $ be any two real numbers in $ [-1, 1] $ such that \[ \cos^{-1}x - \sin^{-1}y = \alpha, \, -\frac{\pi}{2} \leq \alpha \leq \pi. \] Then, the minimum value of $ x^2 + y^2 + 2xy \sin \alpha $ is:

If the domain of the function $f(x) = \sin^{-1}\left( \frac{x - 1}{2x + 3} \right)$ is $\mathbb{R} - (\alpha, \beta)$, then $12 \alpha \beta$ is equal to:

If the domain of the function \[\sin^{-1} \left( \frac{3x - 22}{2x - 19} \right) + \log_e \left( \frac{3x^2 - 8x + 5}{x^2 - 3x - 10} \right)\] is $ (\alpha, \beta] $, then $ 3\alpha + 10\beta $ is equal to:

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation \[ 2 \sin^{-1} x + 3 \cos^{-1} x = \frac{2\pi}{5}, \] is ______ .

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $ x $ satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:

If $a=sin^{-1}(sin\ 5)$ and $b=cos^{-1}(cos\ 5)$, then $a^2+b^2=$

If $sin^{-1}x=2\,tan^{-1}x$ , then the number of integral values of x is equal to:

The range of f(x) = $4\sin^{-1}(\frac{x^2}{x^2+1})$ is

If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___

\[ f(x) = \log_e \left( 4x^2 + 11x + 6 \right) + \sin^{-1} \left( 4x + 3 \right) + \cos^{-1} \left( \frac{10x + 6}{3} \right) \]then $ 36|\alpha + \beta| $ is equal to:

If $\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0<\alpha<13$, then $\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)$ is equal to