Inverse Trigonometric Functions

CBSE Class 12 Mathematics · every board question from this chapter, 2023–2026 · 23 of them repeated across years

• The following graph represents:2026
• The following graph represents:2026
• If tan^-1 x=y, then (dy)/(dx) is equal to:2026
• If 2 cos^-1 x=y, then2026
• The following graph represents:2026
• The domain of f(x)= cos^-1(2 x-5) is:2026
• The principal value of sec^-1(√2)+2 cosec^-1(-√2) is:2026asked 3×
• For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined?2026asked 3×
• The domain of cos^-1(4 x+1) is:2026
• If sin^-1 x+π=y, then2026
• If sin^-1 x=y, then (dy)/(dx) is:2026
• If tan^-1 x=3 y, then2026
• The domain of sin^-1(1-2 x) is:2026
• Evaluate tan [ cos^-1( tan (3 π)/4)].2026
• Evaluate: tan^-1(-1/(√3))+ cot^-1(1/(√3))+ tan^-1( sin (-(π)/2))+ tan^-1( tan (2 π)/3)2026asked 3×
• Evaluate sin [ cos^-1 cos ((7 π)/6)].2026
• Evaluate sin [ tan^-1 tan ((3 π)/4)].2026
• Find the value of sin [ cot^-1 √2( cos ( tan^-1 1))]. OR A relation R on A= 1,2,3 is defined as R= (1,1)(3,3),(1,2). Is R a…2026asked 3×
• Simplify: sin^-1 √(1+ cos 2 x)/2, 0<x<(π)/2. OR Evaluate: cos [ sin^-1(-1)- tan^-1(-√3)].2026
• Simplify: cot^-1 √(1+ cos 2 x)/(1- cos 2 x), x ∈(0, (π)/2). OR Evaluate: sin ( tan^-1(-√3)- sec^-1 2)2026
• Simplify: tan^-1(( cos 2 x- sin 2 x)/( cos 2 x+ sin 2 x)), 0<x<(π)/4. OR Evaluate: tan ( sin^-1 1- cos^-1(-1/2))2026asked 3×
• Find the domain of p(x)= sin^-1(1-2 x^2). Hence, find the value of x for which p(x)=(π)/6. Also, write the range of 2 p(x)+(π)/2.2026
• Find the domain of q(x)= cos^-1(4 x^2-3). Hence, find the value of x for which q(x)=0. Also, write the range of 3 q(x)-π.2026
• Find the domain of g(x)= cos^-1(x^2-1). Hence, find the value of x for which g(x)=(π)/3. Also, write the range of cos^-1 x other…2026
• Domain of sin^-1(2 x^2-3) is:2025
• The principal value of sin^-1( sin (-(10 π)/3)) is:2025
• The principal branch of cos^-1 x is:2025
• Domain of f(x)= cos^-1 x+ sin x is:2025asked 3×
• The value of cos ((π)/6+ cot^-1(-√3)) is2025
• [ sec^-1(-√2)- tan^-1(1/(√3))] is equal to:2025asked 3×
• The principal value of sin^-1( cos (43 π)/5) is2025
• If y= sin^-1 x,-1 ≤ x ≤ 0, then the range of y is2025
• The principal value of cot^-1(-1/(√3)) is:2025asked 3×
• The graph of a trigonometric function is as shown. Which of the following will represent graph of its inverse?2025
• Assertion: Set of values of sec^-1((√3)/2) is a null set. Reason (R): sec^-1 x is defined for x ∈ R-(-1,1).2025asked 3×
• Find the domain of f(x)= sin^-1(-x^2).2025asked 3×
• Find the domain of sec^-1(2 x+1).2025
• Find the domain of the function f(x)= cos^-1(x^2-4).2025
• Find the domain of sin^-1(x^2-3).2025
• Evaluate: tan^-1[2 sin (2 cos^-1 (√3)/2)]2025
• Simplify sin^-1( x√1+x^2). OR Find domain of sin^-1 √x-1.2025asked 3×
• Evaluate: sin^-1( sin (3 π)/5)2025
• Solve for x, 2 tan^-1 x+ sin^-1((2 x)/(1+x^2))=4 √32025
• The derivative of tan^-1(x^2) w.r.t. x is:2024
• Assertion: Domain of y= cos^-1(x) is [-1,1]. Reason (R): The range of the principal value branch of y= cos^-1(x) is [0, π]- (π)/22024asked 3×
• Find value of k if sin^-1[k tan (2 cos^-1 (√3)/2)]=(π)/32024
• Find the value of tan^-1(-1/(√3))+ cot^-1(1/(√3))+ tan^-1[ sin (-(π)/2)]. OR Find the domain of the function f(x)= sin^-1(x^2-4).…2024asked 2×
• Express tan^-1(( cos x)/(1- sin x)), where (-π)/2<x<(π)/2 in the simplest form. OR Find the principal value of tan^-1(1)+…2024asked 3×
• If a= sin^-1((√2)/2)+ cos^-1(-1/2) and b= tan^-1(√3)- cot^-1(-1/(√3)) then find the value of a+b.2024
• Evaluate: sec^2( tan^-1 1/2)+cosec^2( cot^-1 1/3)2024
• Simplify: cos^-1 x+ cos^-1[x/2+ √3-3 x^22]; 1/2 ≤ x ≤ 12024
• Evaluate: cot^2 cosec^-1 3 + sin^2 cos^-1(1/3)2024
• Find the value of sin^-1(-1/2)+ cos^-1(-(√3)/2)+ cot^-1( tan (4 π)/3). OR Find the domain of f(x)= cos^-1(1-x^2). Also, find its…2024
• Find the value of [ sin^2 cos^-1(3/5) + tan^2 sec^-1(3) ].2024
• If a function f: X → Y defined as f(x)=y is one-one and onto, then we can define a unique function g: Y → X such that g(y)=x,…2024asked 3×
• sin [(π)/3+ sin^-1(1/2)] is equal to2023asked 3×
• Assertion: Maximum value of ( cos^-1 x)^2 is π^2. Reason (R): Range of the principal value branch of cos^-1 x is [(-π)/2, (π)/2].2023asked 3×
• Assertion: Range of [ sin^-1 x+2 cos^-1 x] is [0, π]. Reason ( R ): Principal value branch of sin^-1 x has range [-(π)/2, (π)/2].2023asked 3×
• Assertion: The range of the function f(x)=2 sin^-1 x+(3 π)/2, where x ∈[-1,1], is [(π)/2, (5 π)/2]. Reason ( R ): The range of…2023asked 2×
• Assertion: All trigonometric functions have their inverses over their respective domains. Reason (R): The inverse of tan^-1 x…2023asked 3×
• Evaluate sin^-1( sin (3 π)/4)+ cos^-1( cos π)+ tan^-1(1) OR Draw the graph of cos^-1 x, where x ∈[-1,0]. Also, write its range. 22023asked 3×
• Write the domain and range (principle value branch) of the following functions: f(x)= tan^-1 x2023
• Draw the graph of the principal branch of the function f(x)= cos^-1 x.2023
• Find the domain of y= sin^-1(x^2-4). OR Evaluate: cos^-1[ cos (-(7 π)/3)]2023asked 3×
• Find the value of tan^-1[2 cos (2 sin^-1 1/2)]+ tan^-1 1.2023
• Evaluate: 3 sin^-1(1/(√2))+2 cos^-1((√3)/2)+ cos^-1(0) OR Draw the graph of f(x)= sin^-1 x, x ∈[-1/(√2), 1/(√2)]. Also, write…2023asked 3×

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