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MHT CET202519 Apr 2025Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If A = 1 x (x^2+x+1 ) , B = x x^2+x+1 and C = x⁻¹+x⁻²+x⁻³ then

Options

  1. AA+B=C
  2. BA+B=2 C
  3. CA+B=3 C
  4. DA+B=4 C

Correct answer

A. A+B=C

Step-by-step solution

Simplify C : Given C = x⁻¹+x⁻²+x⁻³ , express with common denominator x^3 : C = x^2+x+1 x^3 = x^2+x+1 x^ 3/2 Compute (A+B) : Using A = 1 x x^2+x+1 and B = x x^2+x+1 , the sum is: A + B = 1+x x x^2+x+1 The product simplifies to: A B = 1 x^2+x+1 Applying the tangent addition formula: (A+B) = 1+x x x^2+x+1 1 - 1 x^2+x+1 = 1+x x x^2+x+1 x^2+x+1 x^2+x Factoring and simplifying: (A+B) = 1+x x x^2+x+1 ( x^2+x+1 )^2 x(1+x) = x^2+x+1 x^ 3/2 Conclusion: Since (A+B) = C , it follows that A+B=C .

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