Inverse Trigonometric Functions: JEE Questions & Solutions

If the domain of the function f(x) = cos⁻¹((2x-5)/(11-3x)) + sin⁻¹(2x²-3x+1) is the interval [α, β], then α + 2β is equal to:

Let the maximum value of (sin⁻¹x)² + (cos⁻¹x)² for x ∈ [ -√3/2, 1/√2 ] be m/nπ², where gcd(m, n) = 1. Then m + n is equal to.

The number of solutions of tan⁻¹(4x) + tan⁻¹(6x) = π/6, where -1/2√6 < x < 1/2√6, is equal to

If the domain of the function f(x)=sin⁻¹ (1/(x²-2x-2)) is (-∞,α)∪[β,γ]∪[δ,∞), then α+β+γ+δ is equal to

If k=tan (π/4+1/2cos⁻¹ (2/3)) +tan (1/2sin⁻¹ (2/3)), then the number of solutions of the equation sin⁻¹(kx-1)=sin⁻¹x-cos⁻¹x is:

Considering the principal values of inverse trigonometric functions, the value of tan (2sin⁻¹ 2/√13-2cos⁻¹ 3/√10) is equal to:

Using the principal values of the inverse trigonometric functions the sum of the maximum and the minimum values of…

If π/2 ≤ x ≤ 3π/4, then cos⁻¹ ( 12/13 cos x + 5/13 sin x) is equal to:

If α > β > γ > 0, then the expression cot⁻¹( β + (1 + β²)/(α - β)) + cot⁻¹( γ + (1 + γ²)/(β - γ)) + cot⁻¹( α + (1 + α²)/(γ - α)) is equal…

The value of cos ( sin⁻¹ (3/5) + sin⁻¹ (5/13) + sin⁻¹ (33/65)) is:

Let S = { x: cos⁻¹x = π + sin⁻¹x + sin⁻¹(2x+1) }. Then Σ_(x ∈ S) (2x - 1)² is equal to:

If y = cos(π/3 + cos⁻¹x/2), then (x - y)² + 3y² is equal to.

Considering the principal values of the inverse trigonometric functions, sin⁻¹ ( √3/2 x + 1/2 √(1-x²)), -1/2 < x < 1/√2, is equal to

The value of cot⁻¹ ( (√(1 + tan²(2)) - 1)/tan(2)) - cot⁻¹ ( (√(1 + tan² ( 1/2)) + 1)/(tan ( 1/2))) is equal to:

Considering only the principal values of inverse trigonometric functions, the number of positive real values of x satisfying arctan(x) +…

Let x = m/n (m, n are co-prime natural numbers) be a solution of the equation cos(2sin⁻¹ x) = 1/9, and let α, β (α > β) be the roots of the…

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2sin⁻¹(x) + 3cos⁻¹(x) = 2π/5 is:

If the sum of all the solutions of tan⁻¹(2x/(1-x²)) + cot⁻¹((1-x²)/2x) = π/3, where -1 < x < 1, x ≠ 0, is α - 4/√3, then α is equal to.

Let a₁ = 1, a₂, a₃, a₄, … be consecutive natural numbers. Then tan⁻¹ ( 1/(1 + a₁ a₂)) + tan⁻¹ ( 1/(1 + a₂ a₃)) + … + tan⁻¹ ( 1/(1 +…

If sin⁻¹ ( α/17) + cos⁻¹ ( 4/5) - tan⁻¹ ( 77/36) = 0, 0 < α < 13, then sin⁻¹ (sin α) + cos⁻¹ (cos α) is equal to:

Let (a, b) ⊂ (0, 2π) be the largest interval for which sin⁻¹(sin θ) - cos⁻¹(sin θ) > 0, θ ∈ (0, 2π) holds. If α x² + β x + sin⁻¹( x² - 6x +…

Let S be the set of all solutions of the equation cos⁻¹(2x) - 2cos⁻¹(√(1 - x²)) = π, x ∈ [ -1/2, 1/2 ]. Then Σ_(x ∈ S) 2 sin⁻¹(x² - 1) is…

Let S = {x ∈ ℝ: 0 < x < 1 and 2 tan⁻¹((1-x)/(1+x)) = cos⁻¹((1-x²)/(1+x²))}. If n(S) denotes the number of elements in S, then:

The range of f(x) = 4 sin⁻¹ ( x²/(x² + 1)) is: