Inverse Trigonometric Functions — JEE Main PYQs

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

If the domain of the function $f (x) = cos^{- 1} (\frac{2 x - 5}{11 - 3 x}) + sin^{- 1} (2 x^{2} - 3 x + 1)$ is the interval $[α, β]$ , then $α + 2 β$ is equal to :
JEE Main 2026View solution →
The number of solutions of $tan^{- 1} 4 x + tan^{- 1} 6 x = \frac{π}{6}$ , where $- \frac{1}{2 6} < x < \frac{1}{2 6}$ is equal to
JEE Main 2026View solution →
If the domain of the function $f (x) = sin^{- 1} (\frac{1}{x ^{2} - 2 x - 2})$ , is $(- \infty, α] \cup [β, γ] \cup [δ, \infty)$ , then $α + β + γ + δ$ is equal to
JEE Main 2026View solution →
If $k = tan (\frac{π}{4} + \frac{1}{2} cos^{- 1} (\frac{2}{3})) + tan (\frac{1}{2} sin^{- 1} (\frac{2}{3}))$ then the number of solutions of the equation …
JEE Main 2026View solution →
Considering the principal values of inverse trigonometric functions, the value of the expression $tan (2 sin^{- 1} (\frac{2}{13}) - 2 cos^{- 1} (\frac{3}{10}))$ is equal to :
JEE Main 2026View solution →
Let [ • ] denote the greatest integer function. If the domain of the function $f (x) = cos^{- 1} (\frac{4 x + 2 [ x ]}{3})$ is $[α, β]$ , then $12 (α + β)$ is equal to :
JEE Main 2026View solution →
If $y = tan^{- 1} (\frac{3 c o s x - 4 s i n x}{4 c o s x + 3 s i n x}) + 2 tan^{- 1} (\frac{x}{1 + 1 - x ^{2}})$ , then $\frac{d y}{d x}$ at $x = \frac{3}{2}$ is equal to :
JEE Main 2026View solution →
If $\frac{π}{4} + \sum_{p = 1}^{11} tan^{- 1} (\frac{2 ^{p - 1}}{1 + 2 ^{2 p - 1}}) = α$ , then $tan α$ is equal to ______.
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If $sin (tan^{- 1} (x 2)) = cot (sin^{- 1} 1 - x^{2}), x \in (0, 1)$ , then the value of x is :
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Let $0 < α < 1, β = \frac{1}{3 α}$ and $tan^{- 1} (1 - α) + tan^{- 1} (1 - β) = \frac{π}{4}$ . Then $6 (α + β)$ is equal to:
JEE Main 2026View solution →
Let $α = 3 sin^{- 1} (\frac{6}{11})$ and $β = 3 cos^{- 1} (\frac{4}{9})$ , where inverse trigonometric functions take only the principal values.

Given below are two statements:
Statement I : $cos (α + β) > 0$
Statement II : …
JEE Main 2026View solution →
Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of $16 ((sec^{- 1} x)^{2} + (cosec^{- 1} x)^{2})$ is :
JEE Main 2025View solution →
If $\frac{π}{2} \leq x \leq \frac{3 π}{4}$ , then $cos^{- 1} (\frac{12}{13} cos x + \frac{5}{13} sin x)$ is equal to
JEE Main 2025View solution →
Let $S = {x : cos^{- 1} x = π + sin^{- 1} x + sin^{- 1} (2 x + 1)}$ .

Then $\sum_{x \in S} (2 x - 1)^{2}$ is equal to ______.
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Let $[x]$ denote the greatest integer less than or equal to x . Then domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is :
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$cos (sin^{- 1} \frac{3}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{33}{65})$ is equal to :
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If $α > β > γ > 0$ , then the expression
$cot^{- 1} {β + \frac{( 1 + β ^{2} )}{( α - β )}} + cot^{- 1} {γ + \frac{( 1 + γ ^{2} )}{( β - γ )}}$ …
JEE Main 2025View solution →
If for some $α, β; α \leq β, α + β = 8$ and $sec^{2} (tan^{- 1} α) + cosec^{2} (cot^{- 1} β) = 36$ , then $α^{2} + β$ is ____.
JEE Main 2025View solution →
If $y = cos (\frac{π}{3} + cos^{- 1} \frac{x}{2})$ , then $(x - y)^{2} + 3 y^{2}$ is equal to ______.
JEE Main 2025View solution →
Considering the principal values of the inverse trigonometric functions, $sin^{- 1} (\frac{3}{2} x + \frac{1}{2} 1 - x^{2}), - \frac{1}{2} < x < \frac{1}{2}$ , is equal to
JEE Main 2025View solution →
The value of $cot^{- 1} (\frac{1 + t a n ^{2} ( 2 ) - 1}{t a n ( 2 )}) - cot^{- 1} (\frac{1 + t a n ^{2} ( \frac{1}{2} ) + 1}{t a n ( \frac{1}{2} )})$ is equal to
JEE Main 2025View solution →
Let the domain of the function $f (x) = cos^{- 1} (\frac{4 x + 5}{3 x - 7})$ be $[α, β]$ and the domain of $g (x) = lo g_{2} (2 - 6 lo g_{27} (2 x + 5))$ be $(γ, δ)$ . Then $∣7 (α + β) + 4 (γ + δ) ∣$ is equal to ______
JEE Main 2025View solution →
If the domain of the function $sin^{- 1} (\frac{3 x - 22}{2 x - 19}) + lo g_{e} (\frac{3 x ^{2} - 8 x + 5}{x ^{2} - 3 x - 10})$ is $(α, β]$ , then $3 α + 10 β$ is equal to
JEE Main 2024View solution →
Given that the inverse trigonometric function assumes principal values only. Let $x, y$ be any two real numbers in $[- 1, 1]$ such that $cos^{- 1} x - sin^{- 1} y = α$ , $- \frac{π}{2} \leq α \leq π$ . Then, the minimum value of $x^{2} + y^{2} + 2 x y sin α$ is
JEE Main 2024View solution →
For $n \in N$ , if $cot^{- 1} 3 + cot^{- 1} 4 + cot^{- 1} 5 + cot^{- 1} n = \frac{π}{4}$ , then $n$ is equal to ____.
JEE Main 2024View solution →
If the domain of the function
$f (x) = sin^{- 1} (\frac{x - 1}{2 x + 3})$ is $R - (α, β)$
then $12 α β$ is equal to :
JEE Main 2024View solution →
The integral $\int_{1/4}^{3/4} cos (2 cot^{- 1} \frac{1 - x}{1 + x}) dx$ is equal to:
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Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $2 sin^{- 1} x + 3 cos^{- 1} x = \frac{2 π}{5}$ , is ____.
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Let $x = \frac{m}{n}$ ( m , n are co-prime natural numbers) be a solution of the equation $cos (2 sin^{- 1} x) = \frac{1}{9}$ and let $α, β (α > β)$ be the roots of the equation …
JEE Main 2024View solution →
If $a = sin^{- 1} (sin (5))$ and $b = cos^{- 1} (cos (5))$ , then $a^{2} + b^{2}$ is equal to
JEE Main 2024View solution →
If the domain of the function $f (x) = cos^{- 1} (\frac{2 - ∣ x ∣}{4}) + (lo g_{e} (3 - x))^{- 1}$ is $[- α, β) - {γ}$ , then $α + β + γ$ is equal to :
JEE Main 2024View solution →
Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $tan^{- 1} (x) + tan^{- 1} (2 x) = \frac{π}{4}$ is :
JEE Main 2024View solution →
For $α, β, γ \neq = 0$ , if $sin^{- 1} α + sin^{- 1} β + sin^{- 1} γ = π$ and $(α + β + γ) (α - γ + β) = 3 α β$ , then $γ$ equals
JEE Main 2024View solution →
If the domain of the function $f (x) = sec^{- 1} (\frac{2 x}{5 x + 3})$ is $[α, β) \cup (γ, δ]$ , then $∣3 α + 10 (β + γ) + 21 δ ∣$ is equal to ______.
JEE Main 2023View solution →
The range of $f (x) = 4 sin^{- 1} (\frac{x ^{2}}{x ^{2} + 1})$ is
JEE Main 2023View solution →
For $x \in (- 1, 1]$ , the number of solutions of the equation $sin^{- 1} x = 2 tan^{- 1} x$ is equal to ______.
JEE Main 2023View solution →
If $S = {x \in R : sin^{- 1} (\frac{x + 1}{x ^{2} + 2 x + 2}) - sin^{- 1} (\frac{x}{x ^{2} + 1}) = \frac{π}{4}}$ , then $\sum_{x \in S} (sin ((x^{2} + x + 5) \frac{π}{2}) - cos ((x^{2} + x + 5) π))$ is equal to __ …
JEE Main 2023View solution →
$tan^{- 1} (\frac{1 + 3}{3 + 3}) + sec^{- 1} (\frac{8 + 4 3}{6 + 3 3})$ is equal to
JEE Main 2023View solution →
Let $S = {x \in R : 0 < x < 1 and 2 tan^{- 1} (\frac{1 - x}{1 + x}) = cos^{- 1} (\frac{1 - x ^{2}}{1 + x ^{2}})}$ . If $n (S)$ denotes the number of elements in S th …
JEE Main 2023View solution →
Let $(a, b) \subset (0, 2 π)$ be the largest interval for which
$sin^{- 1} (sin θ) - cos^{- 1} (sin θ) > 0, θ \in (0, 2 π)$ , holds. If …
JEE Main 2023View solution →
Let $a_{1} = 1, a_{2}, a_{3}, a_{4}, \dots$ . be consecutive natural numbers. Then …
JEE Main 2023View solution →
If $sin^{- 1} \frac{α}{17} + cos^{- 1} \frac{4}{5} - tan^{- 1} \frac{77}{36} = 0, 0 < α < 13$ , then $sin^{- 1} (sin α) + cos^{- 1} (cos α)$ is equal to
JEE Main 2023View solution →
Let S be the set of all solutions of the equation $cos^{- 1} (2 x) - 2 cos^{- 1} (1 - x^{2}) = π, x \in [- \frac{1}{2}, \frac{1}{2}]$ . Then $\sum_{x \in S} 2 sin^{- 1} (x^{2} - 1)$ is equal to
JEE Main 2023View solution →
If the sum of all the solutions of
$tan^{- 1} (\frac{2 x}{1 - x ^{2}}) + cot^{- 1} (\frac{1 - x ^{2}}{2 x}) = \frac{π}{3}$ ,
$- 1 < x < 1, x \neq = 0$ , is $α - \frac{4}{3}$ , then $α$ is equal to ______.
JEE Main 2023View solution →
The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :
JEE Main 2022View solution →
Considering only the principal values of the inverse trigonometric functions, the domain of the function $f (x) = cos^{- 1} (\frac{x ^{2} - 4 x + 2}{x ^{2} + 3})$ is :
JEE Main 2022View solution →
Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $cos^{- 1} (x) - 2 sin^{- 1} (x) = cos^{- 1} (2 x)$ is equal to :
JEE Main 2022View solution →
For $k \in R$ , let the solutions of the equation $cos (sin^{- 1} (x cot (tan^{- 1} (cos (sin^{- 1} x))))) = k$ , $0 < ∣ x ∣ < \frac{1}{2}$ be $α$ and $β$ , where the inverse trigonometric functions take only p …
JEE Main 2022View solution →
If $0 < x < \frac{1}{2}$ and $\frac{s i n ^{- 1} x}{α} = \frac{c o s ^{- 1} x}{β}$ , then a value of $sin (\frac{2 π α}{α + β})$ is
JEE Main 2022View solution →
Let $x = sin (2 tan^{- 1} α)$ and $y = sin (\frac{1}{2} tan^{- 1} \frac{4}{3})$ . If $S = {α \in R : y^{2} = 1 - x}$ , then $\sum_{α \in S} 16 α^{3}$ is equal to
JEE Main 2022View solution →