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COMEDK202510 May 2025Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If ( A+ B=- 21 65 , A+ B=- 27 65 ) and ( < A-B < 3 ), then the value of ( ( A-B 2 ) ) is

Options

  1. A6 65
  2. B3 130
  3. C- 3 130
  4. D- 6 65

Correct answer

C. - 3 130

Step-by-step solution

Given A + B = - 21 65 and A + B = - 27 65 . Using sum-to-product formulas: 2 ( A+B 2 ) ( A-B 2 ) = - 21 65 (1) 2 ( A+B 2 ) ( A-B 2 ) = - 27 65 (2) Squaring and adding (1) and (2): 4 ^2 ( A-B 2 ) [ ^2 ( A+B 2 ) + ^2 ( A+B 2 )] = (- 21 65 )^2 + (- 27 65 )^2 4 ^2 ( A-B 2 ) = 441 + 729 65^2 = 1170 4225 = 18 65 ^2 ( A-B 2 ) = 18 4 65 = 9 130 Taking the square root: ( A-B 2 ) = 3 130 Given In this interval, the cosine function is negative. Therefore, ( A-B 2 ) = - 3 130 . Answer: - 3 130

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