Trigonometry · JEE Advanced previous year questions

2023 3 questions

1. Q82023 · 4 Jun 2023 · Paper 1· Numerical answer

   Let ${\tan }^{-1}(x)\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, for $x\in \mathbb{R}$. Then the number of real solutions of the equation $$\sqrt{1+\cos (2x)}=\sqrt{2}{\tan }^{-1}(\tan x)$$ in the set $\left(-\frac{3\pi }{2},-\frac{\pi }{2}\right)\cup \left(-\frac{\pi }{2},\frac{\pi }{2}\right)\cup \left(\frac{\pi }{2},\frac{3\pi }{2}\right)$ is equal to ____.

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   Answer: 3

2. Q112023 · 4 Jun 2023 · Paper 1· Numerical answer

   Let $A=\left\{\frac{1967+1686i\sin \theta }{7-3i\cos \theta }:\theta \in \mathbb{R}\right\}$. If $A$ contains exactly one positive integer $n$, then the value of $n$ is ____.

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   Answer: 281

3. Q32023 · 4 Jun 2023 · Paper 2

   For any $y\in \mathbb{R}$, let ${\cot }^{-1}(y)\in (0,\pi )$ and ${\tan }^{-1}(y)\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$. Then the sum of all the solutions of the equation ${\tan }^{-1}\left(\frac{6y}{9-y^2}\right)+{\cot }^{-1}\left(\frac{9-y^2}{6y}\right)=\frac{2\pi }{3}$ for $0<|y|<3$, is equal to

   1. A.$2\sqrt{3}-3$
   2. B.$3-2\sqrt{3}$
   3. C.$4\sqrt{3}-6$
   4. D.$6-4\sqrt{3}$
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   Answer: C