Lakshya JEE 2.0 (2024) Inverse Trigonometric Functions
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Questions and Answers

What is the domain of the function f(x) = sin^(-1)(2x) + sin^(-1)((1/2) - (1/4))?

  • [-1/2, 1]
  • [-1, 1/2] (correct)
  • [-1/4, 1/2]
  • [-1/2, 1/4]
  • What is the value of x in the equation tan^-1x + 2cot^-1x = πab + c(b - a) / (a + b)?

  • 1/3
  • -(1/3)
  • 2
  • 3 (correct)
  • What is the value of the expression sin^(-1)(sin(5π/7)) + cos^(-1)(cos(5π/7))?

  • π/3
  • π/2
  • π/7
  • 0 (correct)
  • What is the value of 'a' for which the equation ax^2 + sin^-1x^2 - 2x + 2 + cos^-1x^2 - 2x + 2 = 0 has a real solution?

    <p>π/2</p> Signup and view all the answers

    What is the value of cos^(-1)(cos(cos^(-1)(cos(x)))) where x ∈ [0, π/2]?

    <p>x</p> Signup and view all the answers

    What is the value of sin^(-1)(sin(12)) + cos^(-1)(cos(12))?

    <p>0</p> Signup and view all the answers

    What is the value of cos^2θ - sinθ if tan^-1sin2θ - 2sinθ + 3 + cot^-1(5secy + 1) = 2?

    <p>1</p> Signup and view all the answers

    What is the value of sin(2cos^(-1)(x) + sin^(-1)(x)) when x = 1/5?

    <p>1/5</p> Signup and view all the answers

    What is the range of k for which the equation 5 arctan(x^2 + x + k) + 3 arccot(x^2 + x + k) = 2π has two distinct solutions?

    <p>(-∞, 4)</p> Signup and view all the answers

    What is the value of x in the equation tan^-1x + 2cot^-1x = πab + c(b - a) / (a + b)?

    <p>3</p> Signup and view all the answers

    If a sin^(-1)(x) - b cos^(-1)(x) = c, then what is the value of a sin^(-1)(x) + b cos^(-1)(x)?

    <p>0</p> Signup and view all the answers

    What is the value of 'a' for which the equation ax^2 + sin^-1x^2 - 2x + 2 + cos^-1x^2 - 2x + 2 = 0 has a real solution?

    <p>π/2</p> Signup and view all the answers

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