Inverse Trigonometric Functions PYQs - Last 10 Years
JEE Advanced / Mathematics / Trigonometry / 9 recent questions
MathematicsTrigonometry2017-2026
Practice 9 JEE Advanced Mathematics questions from Inverse Trigonometric Functions. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
9
PYQs on Page
Mathematics / Trigonometry
2018-2026
Year Range
Based on indexed question metadata
6
Last 5 Years
2022-2026
9
Last 10 Years
2017-2026
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2019
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Question Types
9PYQs
INTEGER44.4%
MCQ44.4%
MCQM11.1%
Difficulty Mix
#1 Hard5
#2 Medium3
#3 Easy1
6 in last 5 years9 in last 10 years
Last 10 Years Inverse Trigonometric Functions Questions
Showing 9 of 9 filtered questions.
1Inverse Trigonometric Functions
Considering only the principal values of the inverse trigonometric functions, the value of \(\cot^{-1}(\cot(-11)) + 10 \sin\left(2 \cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right) + 10\sin(2 \tan^{-1}(2))\)is
MCQ+3 / -12026
2Inverse Trigonometric Functions
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} ...
$ \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} ...
MCQ+3 / -12025
3Inverse Trigonometric Functions
Considering only the principal values of the inverse trigonometric functions, the value of
\(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)\)
is
\(\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)-2 \cos ^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)\)
is
MCQ+3 / -12024
4Inverse Trigonometric Functions
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{6 y}{9-y^2}\right)+\cot ^{-1}\left(\frac...
MCQ+3 / -12023
5Inverse Trigonometric Functions
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 $\sqrt{1+\cos (2 x)}=\sqrt{2} \tan ^{-1}(\tan x)$ in the set $\left(-\frac{3 \pi}{2},-\frac{\pi}{2}...
INTEGER+4 / -02023
6Inverse Trigonometric Functions
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
\(\frac{3}{2} \cos ^{-1} \sqrt{\frac{2}{2+\pi^{2}}}+\frac{1}{4} \sin ^{-1} \frac{2 \sqrt{2} \pi}{2+\pi^{2}}+\tan ^{-1} \frac{\sqrt{2}}{\pi}\)
is
INTEGER+3 / -02022
7Inverse Trigonometric Functions
The value of $${\sec ^{ - 1}}\left( \matrix{
{1 \over 4}\sum\limits_{k = 0}^{10} {\sec \left( {{{7\pi } \over {12}} + {{k\pi } \over 2}} \right)}
\sec \left( {{{7\pi } \over {12}} + {{(k + 1)\pi } \over 2}} \right) \hfill \cr} \right)...
{1 \over 4}\sum\limits_{k = 0}^{10} {\sec \left( {{{7\pi } \over {12}} + {{k\pi } \over 2}} \right)}
\sec \left( {{{7\pi } \over {12}} + {{(k + 1)\pi } \over 2}} \right) \hfill \cr} \right)...
INTEGER+3 / -02019
8Inverse Trigonometric Functions
For any positive integer n, define \({f_n}:(0,\infty ) \to R\) as\({f_n} = \sum\limits_{j = 1}^n {{{\tan }^{ - 1}}} \left( {{1 \over {1 + (x + j)(x + j - 1)}}} \right)\)for all x\(\in\)(0, \(\infty\)). (Here, the inverse trigonometric fu...
MCQM+4 / -22018
9Inverse Trigonometric Functions
The number of real solutions of the equation $$\eqalign{
& {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = 1}^\infty {} {{\left( {{x \over 2}} \right)}^i}} \right) \cr
& = {\pi \over 2} - {\cos ...
& {\sin ^{ - 1}}\left( {\sum\limits_{i = 1}^\infty {} {x^{i + 1}} - x\sum\limits_{i = 1}^\infty {} {{\left( {{x \over 2}} \right)}^i}} \right) \cr
& = {\pi \over 2} - {\cos ...
INTEGER+3 / -02018