Inverse Trigonometric Functions — JEE Advanced PYQs

15 previous year questions on Inverse Trigonometric Functions (Mathematics), newest first. Open any question for its complete step-by-step solution.

Considering only the principal values of the inverse trigonometric functions, the value of $cot^{- 1} (cot (- 11)) + 10 sin (2 cos^{- 1} (\frac{1}{2})) + 10 sin (2 tan^{- 1} (2))$ is
JEE Advanced 2026View solution →
The total number of real solutions of the equation
$θ = tan^{- 1} (2 tan θ) - \frac{1}{2} sin^{- 1} (\frac{6 tan θ}{9 + tan ^{2} θ})$

is
(Here, the inverse trigonometric functions $sin^{- 1} x$ and $tan^{- 1} x$ assume values in …
JEE Advanced 2025View solution →
Considering only the principal values of the inverse trigonometric functions, the value of
$tan (sin^{- 1} (\frac{3}{5}) - 2 cos^{- 1} (\frac{2}{5}))$

is
JEE Advanced 2024View solution →
For any $y \in R$ , let $cot^{- 1} (y) \in (0, π)$ and $tan^{- 1} (y) \in (- \frac{π}{2}, \frac{π}{2})$ . Then the sum of all the solutions of the equation …
JEE Advanced 2023View solution →
Let $tan^{- 1} (x) \in (- \frac{π}{2}, \frac{π}{2})$ , for $x \in R$ . Then the number of real solutions of the equation $1 + cos (2 x) = 2 tan^{- 1} (tan x)$ in the set …
JEE Advanced 2023View solution →
Considering only the principal values of the inverse trigonometric functions, the value of
$\frac{3}{2} cos^{- 1} \frac{2}{2 + π ^{2}} + \frac{1}{4} sin^{- 1} \frac{2 2 π}{2 + π ^{2}} + tan^{- 1} \frac{2}{π}$

is ____.
JEE Advanced 2022View solution →
For any positive integer n, let $S_{n} : (0, \infty) \to R$ be defined by
$S_{n} (x) = \sum_{k = 1}^{n} cot^{- 1} (\frac{1 + k ( k + 1 ) x ^{2}}{x})$ ,
where for any $x \in R, cot^{- 1} x \in (0, π)$ and …
JEE Advanced 2021View solution →
The number of real solutions of the equation $sin^{- 1} (\sum_{i = 1}^{\infty} x^{i + 1} - x \sum_{i = 1}^{\infty} (\frac{x}{2})^{i}) = \frac{π}{2} - cos^{- 1} (\sum_{i = 1}^{\infty} (- \frac{x}{2})^{i} - \sum_{i = 1}^{\infty} (- x)^{i})$ lying in the int …
JEE Advanced 2018View solution →
For any positive integer $n$ , define $f_{n} : (0, \infty) \to R$ as
$f_{n} (x) = j = 1 \sum n tan^{- 1} (\frac{1}{1 + ( x + j ) ( x + j - 1 )}) for all x \in (0, \infty) .$

(Here, the inverse trigonometric function $tan^{- 1} x$ assumes va …
JEE Advanced 2018View solution →
If $α = 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9})$ , where the inverse trigonometric functions take only the principal values, then the correct option(s) is(are)
JEE Advanced 2015View solution →
Let $f : [0, 4 π] \to [0, π]$ be defined by $f (x) = cos^{- 1} (cos x)$ . The number of points $x \in [0, 4 π]$ satisfying the equation
$f (x) = \frac{10 - x}{10}$

Is
JEE Advanced 2014View solution →
The value of $cot (\sum_{n = 1}^{23} cot^{- 1} (1 + \sum_{k = 1}^{n} 2 k))$ is
JEE Advanced 2013View solution →
If $0 < x < 1$ , then
$1 + x^{2} [{x cos (cot^{- 1} x) + sin (cot^{- 1} x)}^{2} - 1]^{\frac{1}{2}} =$
JEE Advanced 2008View solution →
Let the function $g : (- \infty, \infty) \to (- \frac{π}{2}, \frac{π}{2})$ be given by $g (u) = 2 tan^{- 1} (e^{u}) - \frac{π}{2}$ . Then, $g$ is
JEE Advanced 2008View solution →
Let $(x, y)$ be such that
$sin^{- 1} (a x) + cos^{- 1} (y) + cos^{- 1} (b x y) = \frac{π}{2} .$

Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS.

| Column I …
JEE Advanced 2007View solution →