Inverse Trigonometry

13 JEE Main questions · Maths

MathsJEE Main 21 Jan 2026, Shift 1·Q1·MCQ·Moderate
Open
Domain of inverse trigonometric functions
If the domain of the function $f(x) = \cos^{-1}\left(\dfrac{2x-5}{11-3x}\right) + \sin^{-1}(2x^2 - 3x + 1)$ is the interval $[\alpha, \beta]$ , then $\alpha + 2\beta$ is equal to:
1. (1)1
2. (2)3
3. (3)5
4. (4)2
MathsJEE Main 21 Jan 2026, Shift 2·Q23·Numerical·Moderate
Open
Extreme values of inverse trigonometric expressions
Let the maximum value of $(\sin^{-1}x)^2 + (\cos^{-1}x)^2$ for $x \in \left[-\dfrac{\sqrt3}{2}, \dfrac{1}{\sqrt2}\right]$ be $\dfrac{m}{n}\pi^2$ , where $\gcd(m, n) = 1$ . Then $m + n$ is equal to .
MathsJEE Main 22 Jan 2026, Shift 1·Q14·MCQ·Moderate
Open
Domain of inverse trigonometric functions
If the domain of the function $f(x) = \sin^{-1}\left(\frac{5-x}{3+2x}\right) + \frac{1}{\log_e(10-x)}$ is $(-\infty, \alpha] \cup [\beta, \gamma) - \{\delta\}$ , then $6(\alpha + \beta + \gamma + \delta)$ is equal to
1. (1)70
2. (2)66
3. (3)67
4. (4)68
We corrected a printing error in the original paper
Source printed the second term garbled as “ $\dfrac{1}{\log_e(1\text{-}0}$ ” (a stroke through the 1, the closing “ $x)$ ” missing); corrected to the intended “ $\dfrac{1}{\log_e(10-x)}$ ” (the source solution uses $10 - x > 0$ , $10 - x \neq 1$ , and the printed key needs $\gamma = 10$ , $\delta = 9$ ).
MathsJEE Main 22 Jan 2026, Shift 1·Q18·MCQ·Easy–moderate
Open
Inverse tangent sum equations
The number of solutions of $\tan^{-1}4x + \tan^{-1}6x = \dfrac{\pi}{6}$ , where $-\dfrac{1}{2\sqrt6} < x < \dfrac{1}{2\sqrt6}$ is equal to
1. (1)3
2. (2)0
3. (3)1
4. (4)2
MathsJEE Main 24 Jan 2026, Shift 2·Q13·MCQ·Moderate
Open
Domain of inverse trigonometric functions
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
1. (1)2
2. (2)4
3. (3)3
4. (4)5
MathsJEE Main 28 Jan 2026, Shift 1·Q23·Numerical·Moderate
Open
Inverse trigonometric equations
If $k = \tan\left(\frac{\pi}{4} + \frac12\cos^{-1}\left(\frac23\right)\right) + \tan\left(\frac12\sin^{-1}\left(\frac23\right)\right)$ then the number of solutions of the equation $\sin^{-1}(kx - 1) = \sin^{-1}x - \cos^{-1}x$ is .
MathsJEE Main 28 Jan 2026, Shift 2·Q6·MCQ·Easy–moderate
Open
Principal values and multiple angles
Considering the principal values of inverse trigonometric functions, the value of the expression $\tan\left(2\sin^{-1}\left(\dfrac{2}{\sqrt{13}}\right) - 2\cos^{-1}\left(\dfrac{3}{\sqrt{10}}\right)\right)$ is equal to :
1. (1) $-\dfrac{33}{56}$
2. (2) $\dfrac{33}{56}$
3. (3) $\dfrac{16}{63}$
4. (4) $-\dfrac{16}{63}$
MathsJEE Main 4 Apr 2026, Shift 1·Q1·MCQ·Moderate
Open
Domain with greatest integer function
Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x) = \cos^{-1}\left(\dfrac{4x + 2\left[x\right]}{3}\right)$ is $[\alpha, \beta]$ , then $12(\alpha + \beta)$ is equal to:
1. (1)6
2. (2)8
3. (3)9
4. (4)4
MathsJEE Main 5 Apr 2026, Shift 1·Q24·Numerical·Moderate
Open
Telescoping inverse tangent sum
If $\dfrac{\pi}{4} + \displaystyle\sum_{p=1}^{11}\tan^{-1}\left(\frac{2^{p-1}}{1 + 2^{2p-1}}\right) = \alpha$ , then $\tan\alpha$ is equal to .
MathsJEE Main 6 Apr 2026, Shift 1·Q1·MCQ·Moderate
Open
Domain of inverse trigonometric functions
Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x) = \sin^{-1}\left(\dfrac{x + [x]}{3}\right)$ is $[\alpha, \beta)$ , then $\alpha^2 + \beta^2$ is equal to:
1. (1)2
2. (2)5
3. (3)10
4. (4)13
MathsJEE Main 6 Apr 2026, Shift 1·Q13·MCQ·Easy–moderate
Open
Sum of inverse tangents
Let $0 < \alpha < 1$ , $\beta = \dfrac{1}{3\alpha}$ and $\tan^{-1}(1 - \alpha) + \tan^{-1}(1 - \beta) = \dfrac{\pi}{4}$ . Then $6(\alpha + \beta)$ is equal to:
1. (1)6
2. (2)7
3. (3)8
4. (4)9
MathsJEE Main 6 Apr 2026, Shift 2·Q13·MCQ·Easy–moderate
Open
Inverse trigonometric function equations
If $\sin\left(\tan^{-1}(x\sqrt2)\right) = \cot\left(\sin^{-1}\sqrt{1 - x^2}\right)$ , $x \in (0, 1)$ , then the value of $x$ is:
1. (1) $\dfrac12$
2. (2) $\dfrac13$
3. (3) $\dfrac23$
4. (4) $\dfrac58$
MathsJEE Main 8 Apr 2026, Shift 2·Q12·MCQ·Moderate
Open
Principal value ranges
Let $\alpha = 3\sin^{-1}\left(\dfrac{6}{11}\right)$ and $\beta = 3\cos^{-1}\left(\dfrac49\right)$ , where inverse trigonometric functions take only the principal values.
Given below are two statements:
Statement I: $\cos(\alpha + \beta) > 0$
Statement II: $\cos(\alpha) < 0$
In the light of the above statements, choose the correct answer from the options given below:
1. (1)Both Statement I and Statement II are true
2. (2)Both Statement I and Statement II are false
3. (3)Statement I is true but Statement II is false
4. (4)Statement I is false but Statement II is true