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NEST2026MathematicsInverse Trigonometric Functions

If x (0, 1) and ⁻¹ x - ⁻¹ 1 4 = 3 , then x equals

Options

  1. A1 6 (1 + 2 5 )
  2. B1 8 (1 + 3 5 )
  3. C1 6 (1 + 4 3 )
  4. D1 5 (2 + 3 2 )

Correct answer

B. 1 8 (1 + 3 5 )

Step-by-step solution

Given ⁻¹ x - ⁻¹ 1 4 = 3 ⁻¹ x = 3 + ⁻¹ 1 4 Taking sine on both sides: x = ( 3 + ⁻¹ 1 4 ) Using the identity (A + B) = A B + A B : x = ( 3 ) ( ⁻¹ 1 4 ) + ( 3 ) ( ⁻¹ 1 4 ) We know that ( 3 ) = 3 2 and ( 3 ) = 1 2 . Let = ⁻¹ 1 4 , then = 1 4 . Since (0, 2 ) , = 1 - ^2 = 1 - 1 16 = 15 4 . Substituting these values: x = ( 3 2 ) ( 15 4 ) + ( 1 2 ) ( 1 4 ) x = 45 8 + 1 8 x = 3 5 + 1 8 x = 1 8 (1 + 3 5 ) Answer: 1 8 (1 + 3 5 )

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