Exams › JEE Advanced › Maths

What is the interval of x that satisfies the equation 2 arcsin(x) = arcsin(2√(1−x²))?

1. [1/2, 2/2]
2. [-1/√2, 1/√2]
3. [-1, 1]
4. [-∞, −1/√2]

Correct answer: [-1/√2, 1/√2]

Solution

The interval [-1/√2, 1/√2] satisfies the equation 2 arcsin(x) = arcsin(2√(1−x²)) because it falls within the domain where the equation holds true, considering the properties of inverse trigonometric functions.

Related JEE Advanced Maths questions

• How many solutions exist for the equation arcsin(x) + arccos(y) = π/2?
• The value of cot(∑ₙ₌₁²³ cot⁻¹(1 + ∑ₖ₌₁ⁿ 2k)) is -
• For any y ∈ R, let cot⁻¹(y) ∈ (0, π) and tan⁻¹(y) ∈ (−π/2, π/2). Then the sum of all the solutions of the equation tan⁻¹(6y / 9 − y²) + cot⁻¹((9 − y²) / 6y) = 2π/3 for 0 < |y| < 3, is equal to
• Evaluate: lim (n->infinity) tan[ sum from r=1 to n of arctan(1 / (1 + r + r²)) ].
• If integral sqrt(sec²(x) + 3) dx = ln|f(x) + sqrt(4 + f²(x))| + sqrt(3) * sin⁻¹((k*g(x))/2) + C, where C is the integration constant, then which of the following is/are correct?
• Evaluate the integral: integral of 3 / (x² + 3) dx

⚔️ Practice JEE Advanced Maths free + battle 1v1 →