PrepWiser › Learn › Mathematics › Inverse Trigonometric FunctionsInverse Trigonometric Functions — JEE Main PYQs & Practice Questions Inverse Trigonometric Functions is a Mathematics chapter in the JEE Main syllabus. This page brings together 94 previous-year and practice questions on Inverse Trigonometric Functions, organised into 3 topics: Domain and Range, Properties and Identities and Inverse Trigonometric Equations. Most questions come with a step-by-step solution you can work through free in PrepWiser.
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Chapter weightage : how many questions each chapter had per shift in the 2024–26 papers.
Domain and Range If the domain of the function f(x)=log ₑ((2 x-3)/(5+4 x))+sin ⁻¹((4+3 x)/(2-x)) is [α… If the domain of the function sin ⁻¹((3 x-22)/(2 x-19))+log ₑ((3 x²-8 x+5)/(x²-3 x-10))… The domain of the function f(x) = (cos ⁻¹( (x² - 5x + 6)/(x² - 9) ))/(log ₑ(x² - 3x +… If the domain of the function f(x)=sec ⁻¹((2 x)/(5 x+3)) is [α, β) U(γ, δ], then |3… Let the domain of the function f(x)=cos ⁻¹((4 x+5)/(3 x-7)) be [α, β] and the domain of… If the domain of the function f(x)=sin⁻¹(1/(x²-2x-2)), is (-∞,α]∪ [β,γ]∪ [δ,∞), then… If the domain of the function f(x)=cos⁻¹((2x-5)/(11-3x))+sin⁻¹(2x²-3x+1) is the interval… The domain of the function f(x) = sin ⁻¹( (3x² + x - 1)/(x - 1)² ) + cos ⁻¹( (x - 1)/(x… The domain of the function cos ⁻¹( (2sin ⁻¹( 1/(4x² - 1) ))/π ) is : If domain of the function log ₑ((6 x²+5 x+1)/(2 x-1))+cos ⁻¹((2 x²-3 x+4)/(3 x-5)) is… The domain of the function f(x) = sin ⁻¹( (| x | + 5)/(x² + 1) ) is (– ∞, -a]∪[a, ∞)… Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) =… If the domain of the function f(x)=sin ⁻¹((x-1)/(2 x+3)) is R-(α, β), then 12 α β is… The range of f(x)=4 sin ⁻¹(x²/(x²+1)) is If the domain of the function f(x)=cos ⁻¹((2-|x|)/4)+{log ₑ(3-x)}⁻¹ is [-α, β)-{γ}, then… If the domain of the function f(x) = (cos ⁻¹√(x² - x + 1))/√(sin ⁻¹( (2x - 1)/2 )) is… The domain of the function f(x)=sin ⁻¹((x²-3 x+2)/(x²+2 x+7)) is : Considering only the principal values of the inverse trigonometric functions, the domain… Let f(x) = 2cos ⁻¹x + 4cot ⁻¹x - 3x² - 2x + 10, x ∈ [ - 1,1]. If [a, b] is the range of… The domain of the function cosec ⁻¹( (1 + x)/x ) is : Properties and Identities Using the principal values of the inverse trigonometric functions, the sum of the… If a=sin ⁻¹(sin (5)) and b=cos ⁻¹(cos (5)), then a²+b² is equal to Let m and M respectively be the minimum and the maximum values of f(x) = sin ⁻¹2x + sin… Given that the inverse trigonometric function assumes principal values only. Let x, y be… If for some α, β ; α ≤ β, α+β=8 and sec ²(tan ⁻¹ α)+cosec²(cot ⁻¹ β)=36, then α²+β is… cos (sin ⁻¹ 3/5+sin ⁻¹ 5/13+sin ⁻¹ 33/65) is equal to: The value of cot⁻¹ ( (√(1 + tan²(2)) - 1)/tan(2) ) - cot⁻¹ ( (√(1 + tan²(1/2)) +… Let M and m respectively be the maximum and minimum values of the function f(x) = tan⁻¹… The sum of the infinite series cot ⁻¹(7/4)+cot ⁻¹(19/4)+cot ⁻¹(39/4)+cot ⁻¹(67/4)+…. is : If S is the sum of the first 10 terms of the series tan ⁻¹( 1/3 ) + tan ⁻¹( 1/7 ) + tan… Considering the principal values of the inverse trigonometric functions, sin ⁻¹(√3/2… sin ¹( sin 2π/3 ) + cos ⁻¹( cos 7π/6 ) + tan ⁻¹( tan 3π/4 ) is equal to : If y = tan ⁻¹( sec x³ - tan x³ ),π/2 < x³ < 3π/2, then If π/2 ≤ x ≤ (3 π)/4, then cos ⁻¹(12/13 cos x+5/13 sin x) is equal to The value of tan ⁻¹( (cos ( 15π/4 ) - 1)/(sin ( π/4 )) ) is equal to : 50 tan ( 3tan ⁻¹( 1/2 ) + 2cos ⁻¹( 1/√5 ) ) + 4√2 tan ( 1/2tan ⁻¹(2√2 ) ) is equal to… Let g(x)=f(x)+f(1-x) and f^(′ ′)(x) > 0, x ∈(0,1). If g is decreasing in the interval… Let f(x) = 2x + tan ⁻¹x and g(x) = log ₑ(√(1 + x²) + x),x ∈ [0,3]. Then If the inverse trigonometric functions take principal values then cos ⁻¹( 3/10 cos ( tan… Let α = tan ( 5π/16 sin ( 2cos ⁻¹( 1/√5 ) ) ) and β = cos ( sin ⁻¹( 4/5 ) + sec ⁻¹( 5/3… Inverse Trigonometric Equations If cos ⁻¹( y/2 ) = log ₑ( x/5 )⁵, |y| < 2, then : Let S be the set of all solutions of the equation cos ⁻¹(2 x)-2 cos ⁻¹(√(1-x²))=π, x… For k ∈ ℝ, let the solutions of the equation cos (sin ⁻¹(x cot (tan ⁻¹(cos (sin ⁻¹… The number of solutions of tan⁻¹ 4x+tan⁻¹ 6x=π/6, where -1/2√6<x<1/2√6, is equal to : For α, β, γ ≠ 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 Given that the inverse trigonometric functions take principal values only. Then, the… If S={x ∈ ℝ: sin ⁻¹((x+1)/√(x²+2 x+2))-sin ⁻¹(x/√(x²+1))=π/4}, then Σx ∈ s(sin ((x²+x+5)… If π/4+Σₚ₌₁¹¹tan⁻¹(2ᵖ⁻¹/(1+2²ᵖ⁻¹))=α, then tan α is equal to ____ . The sum of possible values of x for tan⁻¹(x + 1) + cot⁻¹( 1/(x - 1) ) = tan⁻¹( 8/31 ) is : Let α=3 sin⁻¹(6/11) and β=3 cos⁻¹(4/9), where inverse trigonometric functions take only… If the sum of all the solutions of tan ⁻¹( 2x/(1 - x²) ) + cot ⁻¹( (1 - x²)/2x ) = π/3… If k=tan (π/4+1/2 cos⁻¹(2/3))+tan (1/2 sin⁻¹(2/3)), then the number of solutions of the… Let S = { x : cos⁻¹ x = π + sin⁻¹ x + sin⁻¹ [2x + 1] } . Then Σ_(x ∈ S) (2x - 1)² is… For x ∈(-1,1], the number of solutions of the equation sin ⁻¹ x=2 tan ⁻¹ x is equal to… If sin (tan⁻¹(x√2))=cot (sin⁻¹√(1-x²)),x∈ (0,1), then the value of x is: The number of real roots of the equation tan ⁻¹√x(x + 1) + sin ⁻¹√(x² + x + 1) = π/4 is : Considering the principal values of inverse trigonometric functions, the value of the… If sin ⁻¹α/17 + cos ⁻¹4/5 - tan ⁻¹77/36 = 0,0 < α < 13, then sin ⁻¹(sin α ) + cos ⁻¹(cos… Let x=m/n (m, n are co-prime natural numbers) be a solution of the equation cos (2 sin… Considering the principal values of the inverse trigonometric functions, the sum of all… More Mathematics chapters Frequently asked questions How many Inverse Trigonometric Functions questions are there for JEE Main? PrepWiser has 94 Inverse Trigonometric Functions questions for JEE Main, grouped into 3 topics such as Domain and Range, Properties and Identities and Inverse Trigonometric Equations.
Are these Inverse Trigonometric Functions questions from previous-year JEE Main papers? Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.
Where can I see the answers and solutions to these Inverse Trigonometric Functions questions? Open any Inverse Trigonometric Functions question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.