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MHT CET202520 Apr 2025Morning ShiftMathematicsInverse Trigonometric FunctionsActual

If ⁻¹ ( x 2 )+ ⁻¹ ( y 2 )+ ⁻¹ ( z 2 )= 2 then x y+y z+z x=

Options

  1. A0
  2. B2
  3. C-1
  4. D4

Correct answer

D. 4

Step-by-step solution

The equation ⁻¹ ( x 2 ) + ⁻¹ ( y 2 ) + ⁻¹ ( z 2 ) = 2 can be analyzed using trigonometric identities. Let A = ⁻¹ ( x 2 ) , B = ⁻¹ ( y 2 ) , and C = ⁻¹ ( z 2 ) , giving A = x 2 , B = y 2 , and C = z 2 . Since A + B + C = 2 , the trigonometric identity A B + B C + C A = 1 holds. Substituting the tangent values yields xy 4 + yz 4 + zx 4 = 1 . Multiplying both sides by 4 gives xy + yz + zx = 4 . Final answer: 4

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