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JEE MainMathematicsInverse Trigonometric Functions

Let x, y, z be real numbers such that 0 < x < y < z . If ⁻¹x + ⁻¹y + ⁻¹z = and x^2 + y^2 + z^2 = 2 , then the value of z is equal to

Options

  1. A0
  2. B2
  3. C3
  4. D1

Correct answer

D. 1

Step-by-step solution

Let A = ⁻¹x, B = ⁻¹y, C = ⁻¹z . Since 0 Given ⁻¹x + ⁻¹y + ⁻¹z = , we get A + B + C = . Also given x^2 + y^2 + z^2 = 2 , which means ^2 A + ^2 B + ^2 C = 2 . In a triangle, the conditional identity for the sum of squares of sines is: ^2 A + ^2 B + ^2 C = 2 + 2 A B C Substituting the given value, we get: 2 = 2 + 2 A B C A B C = 0 Since A, B, C are angles of a triangle and 0 Therefore, z = C = ( 2 ) = 1 . Answer: 1

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