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
- A0
- B2
- C-1
- 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