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MHT CET202522 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

The number of solutions of ⁻¹ (x+ 2 x )- ⁻¹ ( 4 x )- ⁻¹ (x- 2 x )=0 are

Options

  1. A1
  2. B2
  3. C3
  4. D0

Correct answer

B. 2

Step-by-step solution

The equation ⁻¹ (x+ 2 x )- ⁻¹ ( 4 x )- ⁻¹ (x- 2 x )=0 simplifies by rearranging to ⁻¹ (x+ 2 x ) = ⁻¹ ( 4 x )+ ⁻¹ (x- 2 x ) . Applying the identity ⁻¹ A + ⁻¹ B = ⁻¹ ( A+B 1-AB ) for AB Substituting gives the right-hand side as ⁻¹ ( x+ 2 x -3+ 8 x^2 ) . With common denominators, this becomes ⁻¹ ( (x^2+2)x 8-3x^2 ) . Equating arguments requires x+ 2 x = (x^2+2)x 8-3x^2 , valid for x 0 and 8-3x^2 0 . Simplifying leads to 1 x = x 8-3x^2 , so 8-3x^2 = x^2 , giving x^2 = 2 and x = 2 . Both values satisfy the original equa

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