Inverse Trigonometric Functions: JEE Main Mathematics Previous Year Questions

152 previous year questions from Inverse Trigonometric Functions. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. 1.If$S=(x\text{∈}R\text{:}\text{sin}\left(\frac{x+1}{\sqrt{x^2+2x+2}}\right)-{\text{sin}}^{-1}\left(\frac{x}{\sqrt{x^2+1}}\right)=\frac{\pi }{4})$then…
2. 2.The sum of the infinite series…
3. 3.For non-negative integer $n$, let…
4. 4.…
5. 5.If $y=\text{cos}\text{⁡}(\frac{\pi }{3}+{\text{cos}}^{-1}\text{⁡}\frac{x}{2})$, then $\text{(}x-y{\text{)}}^2++3y^2$ is equal to
6. 6.If $\text{cot}\text{⁡}\left({\text{cos}}^{-1}\text{⁡}x\right)=\text{sec}\text{⁡}\left({\text{tan}}^{-1}\text{⁡}\left(\frac{a}{\sqrt{b^2-a^2}}\right)\right)$…
7. 7.Given $0\le x\le \frac{1}{2}$ then the value of…
8. 8.Domain of ${\text{cos}}^{-1}\text{⁡}\text{[}x\text{]}$ is, where [ ] denotes a greatest integer function
9. 9.If $2\text{sin}\text{⁡}{h}^{-1}\left(\frac{a}{\sqrt{1-a^2}}\right)=\text{log}\text{⁡}\left(\frac{1+x}{1-x}\right)$, then $x$ is equal to
10. 10.The value of $x$ which satisfies $\text{sin}\text{⁡}\left({\text{cot}}^{-1}\text{⁡}x\right)=\text{cos}\text{⁡}({\text{tan}}^{-1}\text{⁡}\text{(}1+x\text{)})$ is
11. 11.The value of ${\text{sin}}^{-1}\text{⁡}\left(\text{cos}\text{⁡}\frac{53\pi }{5}\right)$ is
12. 12.If ${\sum }_{r=1}^{50}{\tan }^{-1}\frac{1}{2r^2}=p$, then the value of $\tan p$ is :
13. 13.If $k=\text{tan}(\frac{\pi }{4}+\frac{1}{2}{\text{cos}}^{-1}\left(\frac{2}{3}\right))+\text{tan}\left(\frac{1}{2}{\text{sin}}^{-1}\left(\frac{2}{3}\right)\right)$, then…
14. 14.Considering the principal values of the inverse trigonometric functions,…
15. 15.Let $S=(x\text{:}{\text{cos}}^{-1}\text{⁡}x=\pi +{\text{sin}}^{-1}\text{⁡}x+{\text{sin}}^{-1}\text{⁡}\text{(}2x+1\text{)})$. Then…
16. 16.If ${\text{cos}}^{-1}\text{⁡}x+{\text{cos}}^{-1}\text{⁡}y+{\text{cos}}^{-1}\text{⁡}z=3\pi$, then
17. 17.If $\alpha =3{\text{sin}}^{-1}\left(\frac{6}{11}\right)$ and $\beta =3{\text{cos}}^{-1}\left(\frac{4}{9}\right)$, where the inverse trigonometric functions take only th…
18. 18.The number of solutions of the equation${\text{sin}}^{-1}\text{⁡}(x^2+\frac{1}{3})+{\text{cos}}^{-1}\text{⁡}(x^2-\frac{2}{3})=x^2$ for…
19. 19.If ${\text{tan}}^{-1}\text{⁡}\left(\frac{1}{1+1.2}\right)+{\text{tan}}^{-1}\text{⁡}\left(\frac{1}{1+2.3}\right)+\text{…}+{\text{tan}}^{-1}$…
20. 20.For any $y\text{∈}R$, let ${\text{cot}}^{-1}\text{(}y\text{)}\text{∈}\text{(}0\text{,}\pi \text{)}$ and…
21. 21.If ${\text{sin}}^{-1}\text{⁡}x+{\text{cos}}^{-1}\text{⁡}y=\frac{2\pi }{5}$, then ${\text{cos}}^{-1}\text{⁡}x+{\text{sin}}^{-1}\text{⁡}y$ is
22. 22.${\text{cot}}^{-1}\text{⁡}(2\cdot 1^2)+{\text{cot}}^{-1}\text{⁡}(2\cdot 2^2)+{\text{cot}}^{-1}\text{⁡}(2\cdot 3^2)+\text{…}$ up to $\infty =$
23. 23.If $x=\text{log}\text{⁡}(y+\sqrt{y^2+1})$ then $y=$
24. 24.If ${\text{sin}}^{-1}\text{⁡}x<{\text{cos}}^{-1}\text{⁡}x$, then
25. 25.Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $co{s}^{-1}$(x)-$2si{n}^{-l}$(x) = $co{s}^{-1}$(2x) is equ…