JEE Advanced · 2024 · 26 May 2024 · Paper 2 · Inverse Trigonometric Functions

More JEE Advanced questions on Inverse Trigonometric Functions

1. Considering only the principal values of the inverse trigonometric functions, the value of ${\cot }^{-1}(\cot (-11))+10\sin \left(2{\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)\right)+10\sin \left(2{\tan }^{-1}(2)\right)$ is
   JEE Advanced 2026 Copy linkView solution →
2. The total number of real solutions of the equation
   

   $$\theta ={\tan }^{-1}(2\tan \theta )-\frac{1}{2}{\sin }^{-1}\left(\frac{6\tan \theta }{9+{\tan }^2\theta }\right)$$

   
   is
   (Here, the inverse trigonometric functions ${\sin }^{-1}x$ and ${\tan }^{-1}x$ assume values in …
   JEE Advanced 2025 Copy linkView solution →
3. For any $\mathrm{y}\in \mathbb{R}$, let ${\cot }^{-1}(\mathrm{y})\in (0,\pi )$ and ${\tan }^{-1}(\mathrm{y})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$. Then the sum of all the solutions of the equation …
   JEE Advanced 2023 Copy linkView solution →
4. Let ${\tan }^{-1}(\mathrm{x})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, for $\mathrm{x}\in \mathbb{R}$. Then the number of real solutions of the equation $\sqrt{1+\cos (2x)}=\sqrt{2}{\tan }^{-1}(\tan x)$ in the set …
   JEE Advanced 2023 Copy linkView solution →
5. Considering only the principal values of the inverse trigonometric functions, the value of
   

   $$\frac{3}{2}{\cos }^{-1}\sqrt{\frac{2}{2+{\pi }^2}}+\frac{1}{4}{\sin }^{-1}\frac{2\sqrt{2}\pi }{2+{\pi }^2}+{\tan }^{-1}\frac{\sqrt{2}}{\pi }$$

   
   is ____.
   JEE Advanced 2022 Copy linkView solution →
6. For any positive integer n, let $S_n:(0,\infty )\to \mathbb{R}$ be defined by
   $S_n(x)={\sum }_{k=1}^n{\cot }^{-1}\left(\frac{1+k(k+1)x^2}{x}\right)$,
   where for any $x\in \mathbb{R},{\cot }^{-1}x\in (0,\pi )$ and …
   JEE Advanced 2021 Copy linkView solution →