New chat PYQ Library Doubts Rank report

Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →

Inverse Trigonometric Functions

87 questions · Mathematics · JEE Main

Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.

PYQ Library
JEE Main
Mathematics
Inverse Trigonometric Functions

Inverse Trigonometric Functions

87 questions · Mathematics · JEE Main

$If y = cos (\frac{π}{3} + cos^{- 1} \frac{x}{2}), then (x - y)^{2} + 3 y^{2} is equal to$ 2025 · 2 Apr · Shift 2 · Q46 · Numerical
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 to2025 · 4 Apr · Shift 1 · Q45 · MCQ
The sum of the infinite series $cot^{- 1} (\frac{7}{4}) + cot^{- 1} (\frac{19}{4}) + cot^{- 1} (\frac{39}{4}) + cot^{- 1} (\frac{67}{4}) + \dots$ . is :2025 · 4 Apr · Shift 2 · Q40 · MCQ
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 to2025 · 8 Apr · Shift 2 · Q34 · MCQ
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 :2025 · 22 Jan · Shift 1 · Q42 · MCQ
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 to2025 · 23 Jan · Shift 1 · Q31 · MCQ
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 2025 · 24 Jan · Shift 1 · Q49 · Numerical
If $α > β > γ > 0$ , then the expression $cot^{- 1} {β + \frac{( 1 + β ^{2} )}{( α - β )}} + cot^{- 1} {γ + \frac{( 1 + γ ^{2} )}{( β - γ )}} + cot^{- 1} {α + \frac{( 1 + α ^{2} )}{( γ - α )}}$ …2025 · 24 Jan · Shift 2 · Q32 · MCQ
$cos (sin^{- 1} \frac{3}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{33}{65})$ is equal to:2025 · 28 Jan · Shift 1 · Q31 · MCQ
Let [x] denote the greatest integer less than or equal to x. Then the domain of $f (x) = sec^{- 1} (2 [x] + 1)$ is:2025 · 28 Jan · Shift 2 · Q35 · MCQ
Let S = ${x : cos^{- 1} x = π + sin^{- 1} x + sin^{- 1} [2 x + 1]}$ . Then $x \in S \sum (2 x - 1)^{2}$ is equal to .2025 · 29 Jan · Shift 1 · Q48 · Numerical
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:2024 · 4 Apr · Shift 1 · Q39 · MCQ
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 $x^{2} + y^{2} + 2 x y sin α$ …2024 · 4 Apr · Shift 2 · Q39 · MCQ
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 .2024 · 6 Apr · Shift 1 · Q57 · Numerical
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 .2024 · 9 Apr · Shift 2 · Q59 · Numerical
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 :2024 · 27 Jan · Shift 2 · Q31 · MCQ
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 $m x^{2} - n x - m + n = 0$ . Then the…2024 · 29 Jan · Shift 2 · Q49 · MCQ
For $α, β, γ e q 0$ , if $sin^{- 1} α + sin^{- 1} β + sin^{- 1} γ = π$ and $(α + β + γ) (α - γ + β) = 3 α β$ , then $γ$ equals2024 · 31 Jan · Shift 1 · Q32 · MCQ
If $a = sin^{- 1} (sin (5))$ and $b = cos^{- 1} (cos (5))$ , then $a^{2} + b^{2}$ is equal to2024 · 31 Jan · Shift 2 · Q35 · MCQ
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 :2023 · 1 Feb · Shift 1 · Q23 · MCQ
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 $S$ then :2023 · 1 Feb · Shift 2 · Q37 · MCQ
If the domain of the function $f (x) = sec^{- 1} (\frac{2 x}{5 x + 3})$ is $[α, β) U (γ, δ]$ , then $∣3 α + 10 (β + γ) + 21 δ ∣$ is equal to .2023 · 10 Apr · Shift 2 · Q37 · Numerical
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 $\sum_{x \in s} (sin ((x^{2} + x + 5) \frac{π}{2}) - cos ((x^{2} + x + 5) π))$ …2023 · 13 Apr · Shift 1 · Q41 · Numerical
For $x \in (- 1, 1]$ , the number of solutions of the equation $sin^{- 1} x = 2 tan^{- 1} x$ is equal to .2023 · 13 Apr · Shift 2 · Q40 · Numerical
If the domain of the function $f (x) = lo g_{e} (4 x^{2} + 11 x + 6) + sin^{- 1} (4 x + 3) + cos^{- 1} (\frac{10 x + 6}{3})$ is $(α, β]$ , then $36∣ α + β ∣$ is equal to :2023 · 15 Apr · Shift 1 · Q28 · MCQ
$tan^{- 1} (\frac{1 + 3}{3 + 3}) + sec^{- 1} (\frac{8 + 4 3}{6 + 3 3})$ is equal to :2023 · 24 Jan · Shift 1 · Q28 · MCQ
If the sum of all the solutions of $tan^{- 1} (\frac{2 x}{1 - x ^{2}}) + cot^{- 1} (\frac{1 - x ^{2}}{2 x}) = \frac{π}{3}, - 1 < x < 1, x e 0$ , is $α - \frac{4}{3}$ , then $α$ …2023 · 25 Jan · Shift 1 · Q46 · Numerical
Let $a_{1} = 1, a_{2}, a_{3}, a_{4}, \dots .$ . be consecutive natural numbers. Then $tan^{- 1} (\frac{1}{1 + a _{1} a _{2}}) + tan^{- 1} (\frac{1}{1 + a _{2} a _{3}}) + \dots .. + tan^{- 1} (\frac{1}{1 + a _{2021} a _{2022}})$ …2023 · 30 Jan · Shift 2 · Q23 · Multiple correct
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 :2023 · 31 Jan · Shift 1 · Q27 · MCQ
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 $α x^{2} + β x + sin^{- 1} (x^{2} - 6 x + 10) + cos^{- 1} (x^{2} - 6 x + 10) = 0$ …2023 · 31 Jan · Shift 2 · Q26 · MCQ
The set of all values of k for which $(tan^{- 1} x)^{3} + (cot^{- 1} x)^{3} = k π^{3}, x \in R$ , is the interval :2022 · 24 Jun · Shift 1 · Q28 · MCQ
The domain of the function $f (x) = \frac{c o s ^{- 1} ( \frac{x ^{2} - 5 x + 6}{x ^{2} - 9} )}{l o g _{e} ( x ^{2} - 3 x + 2 )}$ is :2022 · 24 Jun · Shift 1 · Q34 · MCQ
Let $x * y = x^{2} + y^{3}$ and $(x * 1) * 1 = x * (1 * 1)$ . Then a value of $2 sin^{- 1} (\frac{x ^{4} + x ^{2} - 2}{x ^{4} + x ^{2} + 2})$ is :2022 · 24 Jun · Shift 2 · Q22 · MCQ
Let $x = sin (2 tan^{- 1} α)$ and $y = sin (\frac{1}{2} tan^{- 1} \frac{4}{3})$ . If $S = {a \in R : y^{2} = 1 - x}$ , then $α \in S \sum 16 α^{3}$ is equal to …2022 · 25 Jul · Shift 2 · Q45 · Numerical
The value of $tan^{- 1} (\frac{c o s ( \frac{15 π}{4} ) - 1}{s i n ( \frac{π}{4} )})$ is equal to :2022 · 25 Jun · Shift 2 · Q35 · MCQ
$tan (2 tan^{- 1} \frac{1}{5} + sec^{- 1} \frac{5}{2} + 2 tan^{- 1} \frac{1}{8})$ is equal to :2022 · 26 Jul · Shift 1 · Q38 · MCQ
If $0 < x < \frac{1}{2}$ and $\frac{s i n ^{- 1} x}{α} = \frac{c o s ^{- 1} x}{β}$ , then the value of $sin (\frac{2 π α}{α + β})$ is :2022 · 26 Jul · Shift 2 · Q31 · MCQ
If the inverse trigonometric functions take principal values then $cos^{- 1} (\frac{3}{10} cos (tan^{- 1} (\frac{4}{3})) + \frac{2}{5} sin (tan^{- 1} (\frac{4}{3})))$ …2022 · 26 Jun · Shift 2 · Q38 · MCQ
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 $β$ ,…2022 · 27 Jul · Shift 1 · Q39 · Numerical
The domain of the function $f (x) = sin^{- 1} [2 x^{2} - 3] + lo g_{2} (lo g_{\frac{1}{2}} (x^{2} - 5 x + 5))$ , where [t] is the greatest integer function, is :2022 · 27 Jul · Shift 2 · Q22 · MCQ
$sin^{1} (sin \frac{2 π}{3}) + cos^{- 1} (cos \frac{7 π}{6}) + tan^{- 1} (tan \frac{3 π}{4})$ is equal to :2022 · 27 Jun · Shift 1 · Q35 · MCQ
The value of $cot (n = 1 \sum 50 tan^{- 1} (\frac{1}{1 + n + n ^{2}}))$ is :2022 · 27 Jun · Shift 2 · Q35 · MCQ
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 :2022 · 28 Jul · Shift 1 · Q24 · MCQ
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 :2022 · 28 Jul · Shift 1 · Q26 · MCQ
The sum of the absolute maximum and absolute minimum values of the function $f (x) = tan^{- 1} (sin x - cos x)$ in the interval $[0, π]$ is :2022 · 28 Jul · Shift 2 · Q27 · MCQ
The domain of the function $f (x) = sin^{- 1} (\frac{x ^{2} - 3 x + 2}{x ^{2} + 2 x + 7})$ is :2022 · 29 Jul · Shift 2 · Q36 · MCQ
The domain of the function $cos^{- 1} (\frac{2 s i n ^{- 1} ( \frac{1}{4 x ^{2} - 1} )}{π})$ is :2022 · 29 Jun · Shift 1 · Q31 · MCQ
$50 tan (3 tan^{- 1} (\frac{1}{2}) + 2 cos^{- 1} (\frac{1}{5})) + 42 tan (\frac{1}{2} tan^{- 1} (22))$ is equal to …2022 · 29 Jun · Shift 1 · Q38 · Numerical
Let m and M respectively be the minimum and the maximum values of $f (x) = sin^{- 1} 2 x + sin 2 x + cos^{- 1} 2 x + cos 2 x, x \in [0, \frac{π}{8}]$ . Then m + M is equal to :2022 · 30 Jun · Shift 1 · Q30 · MCQ
Let $α = tan (\frac{5 π}{16} sin (2 cos^{- 1} (\frac{1}{5})))$ and $β = cos (sin^{- 1} (\frac{4}{5}) + sec^{- 1} (\frac{5}{3}))$ …2022 · 30 Jun · Shift 1 · Q33 · MCQ
$cos^{- 1} (cos (- 5)) + sin^{- 1} (sin (6)) - tan^{- 1} (tan (12))$ is equal to : (The inverse trigonometric functions take the principal values)2021 · 1 Sep · Shift 2 · Q25 · MCQ
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy $sin^{- 1} (\frac{3 x}{5}) + sin^{- 1} (\frac{4 x}{5}) = sin^{- 1} x$ …2021 · 16 Mar · Shift 2 · Q36 · MCQ
The sum of possible values of x for tan $-$ 1(x + 1) + cot $-$ 1 $(\frac{1}{x - 1})$ = tan $-$ 1 $(\frac{8}{31})$ is :2021 · 17 Mar · Shift 1 · Q27 · MCQ
If cot $-$ 1( $α$ ) = cot $-$ 1 2 + cot $-$ 1 8 + cot $-$ 1 18 + cot $-$ 1 32 + ...... upto 100 terms, then $α$ is :2021 · 17 Mar · Shift 1 · Q34 · MCQ
The number of solutions of the equation $sin^{- 1} [x^{2} + \frac{1}{3}] + cos^{- 1} [x^{2} - \frac{2}{3}] = x^{2}$ , for x $\in$ [ $-$ 1, 1], and [x] denotes the greatest integer less than or equal to…2021 · 17 Mar · Shift 2 · Q25 · MCQ
The number of real roots of the equation $tan^{- 1} x (x + 1) + sin^{- 1} x^{2} + x + 1 = \frac{π}{4}$ is :2021 · 20 Jul · Shift 1 · Q31 · MCQ
The value of $tan (2 tan^{- 1} (\frac{3}{5}) + sin^{- 1} (\frac{5}{13}))$ is equal to :2021 · 20 Jul · Shift 2 · Q25 · MCQ
If the domain of the function $f (x) = \frac{c o s ^{- 1} x ^{2} - x + 1}{s i n ^{- 1} ( \frac{2 x - 1}{2} )}$ is the interval ( $α$ , $β$ ], then $α$ + $β$ is equal to :2021 · 22 Jul · Shift 2 · Q35 · MCQ
A possible value of $tan (\frac{1}{4} sin^{- 1} \frac{63}{8})$ is :2021 · 24 Feb · Shift 2 · Q32 · MCQ
cosec $[2 cot^{- 1} (5) + cos^{- 1} (\frac{4}{5})]$ is equal to :2021 · 25 Feb · Shift 2 · Q31 · MCQ
The domain of the function $cosec o l imi t s^{- 1} (\frac{1 + x}{x})$ is :2021 · 26 Aug · Shift 2 · Q28 · MCQ
If $r = 1 \sum 50 tan^{- 1} \frac{1}{2 r ^{2}} = p$ , then the value of tan p is :2021 · 26 Aug · Shift 2 · Q30 · MCQ
If $\frac{s i n ^{1} x}{a} = \frac{c o s ^{- 1} x}{b} = \frac{t a n ^{- 1} y}{c}$ ; $0 < x < 1$ , then the value of $cos (\frac{π c}{a + b})$ is :2021 · 26 Feb · Shift 1 · Q33 · MCQ
If 0 < a, b < 1, and tan $-$ 1a + tan $-$ 1b = $\frac{π}{4}$ , then the value of $(a + b) - (\frac{a ^{2} + b ^{2}}{2}) + (\frac{a ^{3} + b ^{3}}{3}) - (\frac{a ^{4} + b ^{4}}{4}) + .....$ …2021 · 26 Feb · Shift 2 · Q30 · MCQ
If $(sin^{- 1} x)^{2} - (cos^{- 1} x)^{2} = a$ ; 0 < x < 1, a $e$ 0, then the value of 2x2 $-$ 1 is :2021 · 27 Aug · Shift 1 · Q24 · MCQ
Let M and m respectively be the maximum and minimum values of the function f(x) = tan $-$ 1 (sin x + cos x) in $[0, \frac{π}{2}]$ , then the value of tan(M $-$ m) is equal to :2021 · 27 Aug · Shift 2 · Q25 · MCQ
The domain of the function $f (x) = sin^{- 1} (\frac{3 x ^{2} + x - 1}{( x - 1 ) ^{2}}) + cos^{- 1} (\frac{x - 1}{x + 1})$ is :2021 · 31 Aug · Shift 2 · Q23 · MCQ
The domain of the function f(x) = $sin^{- 1} (\frac{∣ x ∣ + 5}{x ^{2} + 1})$ is (– $\infty$ , -a] $\cup$ [a, $\infty$ ). Then a is equal to :2020 · 2 Sep · Shift 1 · Q33 · MCQ
2 $π$ - $(sin^{- 1} \frac{4}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{16}{65})$ is equal to :2020 · 3 Sep · Shift 1 · Q20 · MCQ
If S is the sum of the first 10 terms of the series $tan^{- 1} (\frac{1}{3}) + tan^{- 1} (\frac{1}{7}) + tan^{- 1} (\frac{1}{13}) + tan^{- 1} (\frac{1}{21}) + ....$ …2020 · 5 Sep · Shift 1 · Q38 · MCQ
If $α = cos^{- 1} (\frac{3}{5})$ , $β = tan^{- 1} (\frac{1}{3})$ where $0 < α, β < \frac{π}{2}$ , then $α$ - $β$ is equal to :2019 · 8 Apr · Shift 1 · Q23 · MCQ
If $cos^{- 1} (\frac{2}{3 x}) + cos^{- 1} (\frac{3}{4 x}) = \frac{π}{2}$ (x > $\frac{3}{4}$ ), then x is equal to :2019 · 9 Jan · Shift 1 · Q28 · MCQ
If x = sin $-$ 1(sin10) and y = cos $-$ 1(cos10), then y $-$ x is equal to :2019 · 9 Jan · Shift 2 · Q42 · MCQ
If $cos^{- 1} x - cos^{- 1} \frac{y}{2} = α$ ,where –1 $\leq$ x $\leq$ 1, – 2 $\leq$ y $\leq$ 2, x $\leq \frac{y}{2}$ , then for all x, y, 4x2 – 4xy cos $α$ + y2 is equal to :2019 · 10 Apr · Shift 2 · Q31 · MCQ
The value of $cot (n = 1 \sum 19 cot^{- 1} (1 + p = 1 \sum n 2 p))$ is :2019 · 10 Jan · Shift 2 · Q40 · MCQ
All x satisfying the inequality (cot–1 x)2– 7(cot–1 x) + 10 > 0, lie in the interval :2019 · 11 Jan · Shift 2 · Q41 · MCQ
The value of $sin^{- 1} (\frac{12}{13}) - sin^{- 1} (\frac{3}{5})$ is equal to :2019 · 12 Apr · Shift 1 · Q32 · MCQ
Considering only the principal values of inverse functions, the set A = { x $\geq$ 0: tan $-$ 1(2x) + tan $-$ 1(3x) = $\frac{π}{4}$ }2019 · 12 Jan · Shift 1 · Q43 · MCQ
The value of tan-1 $[\frac{1 + x ^{2} + 1 - x ^{2}}{1 + x ^{2} - 1 - x ^{2}}], ∣ x ∣ < \frac{1}{2}, x e 0,$ is equal to :2017 · 8 Apr · Shift 1 · Q35 · MCQ
A value of x satisfying the equation sin[cot−1 (1+ x)] = cos [tan−1 x], is :2017 · 9 Apr · Shift 1 · Q34 · MCQ
Let $tan^{- 1} y = tan^{- 1} x + tan^{- 1} (\frac{2 x}{1 - x ^{2}}),$ where $∣ x ∣ < \frac{1}{3} .$ Then a value of $y$ is :2015 · Shift 0 · Q35 · MCQ
If $x, y, z$ are in A.P. and $tan^{- 1} x, tan^{- 1} y$ and $tan^{- 1} z$ are also in A.P., then :2013 · Shift 0 · Q34 · MCQ
The value of $co t (cos e c^{- 1} \frac{5}{3} + tan^{- 1} \frac{2}{3})$ is :2008 · Shift 0 · Q42 · MCQ
If sin-1 $(\frac{x}{5})$ + cosec-1 $(\frac{5}{4})$ = $\frac{π}{2}$ , then the value of x is :2007 · Shift 0 · Q43 · MCQ
If $cos^{- 1} x - cos^{- 1} \frac{y}{2} = α,$ then $4 x^{2} - 4 x y cos α + y^{2}$ is equal to :2005 · Shift 0 · Q83 · MCQ
The trigonometric equation $sin^{- 1} x = 2 sin^{- 1} a$ has a solution for :2003 · Shift 0 · Q77 · MCQ
$cot^{- 1} (cos α) - tan^{- 1} (cos α) = x,$ then sin x is equal to :2002 · Shift 0 · Q76 · MCQ