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COMEDK2022MathematicsTrigonometric Ratios & Identities

If A+ B=a and A+ B=b , then (A+B) equals?

Options

  1. Aa^2+b^2 b^2-a^2
  2. B2 a b a^2+b^2
  3. Cb^2-a^2 a^2+b^2
  4. Da^2-b^2 a^2+b^2

Correct answer

C. b^2-a^2 a^2+b^2

Step-by-step solution

Given A + B = a and A + B = b . Squaring both equations: ( A + B)^2 = a^2 ^2 A + ^2 B + 2 A B = a^2 ( A + B)^2 = b^2 ^2 A + ^2 B + 2 A B = b^2 Adding the two squared equations: ( ^2 A + ^2 A) + ( ^2 B + ^2 B) + 2( A B + A B) = a^2 + b^2 1 + 1 + 2 (A - B) = a^2 + b^2 2 (A - B) = a^2 + b^2 - 2 Subtracting the squared equations ( b^2 - a^2 ): b^2 - a^2 = ( ^2 A + ^2 B + 2 A B) - ( ^2 A + ^2 B + 2 A B) b^2 - a^2 = ( ^2 A - ^2 A) + ( ^2 B - ^2 B) + 2( A B - A B) b^2 - a^2 = 2A + 2B + 2 (A + B) b^2 - a^2 = 2 (A + B) (A -

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