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COMEDK2024Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If x (x-2 y) = then (x-y) y=

Options

  1. A1-
  2. B1+ 1-
  3. C1- 1+
  4. D1+

Correct answer

C. 1- 1+

Step-by-step solution

Given x (x-2y) = . Applying componendo and dividendo: (x-2y) + x (x-2y) - x = 1+ 1- Using the sum-to-product formulas A + B = 2 ( A+B 2 ) ( A-B 2 ) and A - B = -2 ( A+B 2 ) ( A-B 2 ) : 2 ( x-2y+x 2 ) ( x-2y-x 2 ) -2 ( x-2y+x 2 ) ( x-2y-x 2 ) = 1+ 1- 2 (x-y) (-y) -2 (x-y) (-y) = 1+ 1- Since (-y) = y and (-y) = - y , the expression simplifies to: (x-y) y (x-y) y = 1+ 1- (x-y) y = 1+ 1- Taking the reciprocal of both sides: (x-y) y = 1- 1+ Answer: 1- 1+

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