Inverse Trigonometric Functions JEE Main PYQs PDF, 2020–2026

Inverse Trigonometric Functions questions per year

Topic-wise weightage by year

How many Inverse Trigonometric Functions questions each topic had in every JEE Main year (all shifts), counting every question asked, including ones not in the PDF. Darker cells mean more questions.

Swipe the table sideways for older years.

Newest questions (2026)

All 10 JEE Main 2026 Inverse Trigonometric Functions questions in the free PDF, latest shift first.

1. JEE Main 2026 · 8 Apr · Shift 2 · Inverse Trigonometric Equations

   Let $\alpha=3\sin^{{-1}}\left(\frac{6}{11}\right)$ and $\beta=3\cos^{{-1}}\left(\frac{4}{9}\right)$, 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 :

   Solve it online →

2. JEE Main 2026 · 6 Apr · Shift 1 · Inverse Trigonometric Equations

   Let $0<\alpha<1,\beta=\frac{1}{3\alpha}$ and $\tan^{{-1}}(1-\alpha)+\tan^{{-1}}(1-\beta)=\frac{\pi}{4}$. Then $6(\alpha+\beta)$ is equal to:

   Solve it online →

3. JEE Main 2026 · 6 Apr · Shift 2 · Inverse Trigonometric Equations

   If $\sin \left(\tan^{{-1}}(x\sqrt{2})\right)=\cot \left(\sin^{{-1}}\sqrt{1-x^{2}}\right),x\in (0,1)$, then the value of $x$ is:

   Solve it online →

4. JEE Main 2026 · 5 Apr · Shift 1 · Inverse Trigonometric Equations

   If $\frac{\pi}{4}+\sum_{{p=1}}^{{11}}\tan^{{-1}}\left(\frac{2^{{p-1}}}{1+2^{{2p-1}}}\right)=\alpha$, then $\tan \alpha$ is equal to $\_\_\_\_$ .

   Solve it online →

5. JEE Main 2026 · 28 Jan · Shift 1 · Inverse Trigonometric Equations

   If $k=\tan \left(\frac{\pi}{4}+\frac{1}{2}\cos^{{-1}}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2}\sin^{{-1}}\left(\frac{2}{3}\right)\right)$, then
   
   the number of solutions of the equation $\sin^{{-1}}(kx-1)=\sin^{{-1}}x-\cos^{{-1}}x$ is $\_\_\_\_$.

   Solve it online →

6. JEE Main 2026 · 28 Jan · Shift 2 · Inverse Trigonometric Equations

   Considering the principal values of inverse trigonometric functions, the value of the expression

   $\tan \left(2\sin^{{-1}}\left(\frac{2}{\sqrt{13}}\right)-2\cos^{{-1}}\left(\frac{3}{\sqrt{10}}\right)\right)$

   is equal to :

   Solve it online →

7. JEE Main 2026 · 24 Jan · Shift 2 · Domain and Range

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

   Solve it online →

8. JEE Main 2026 · 22 Jan · Shift 1 · Inverse Trigonometric Equations

   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 :

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9. JEE Main 2026 · 21 Jan · Shift 1 · Domain and Range

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

   Solve it online →

10. JEE Main 2026 · 21 Jan · Shift 2 · Inverse Trigonometric Equations

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

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