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MHT CET202620 April 2026Morning ShiftMathematicsTrigonometric EquationsActual

The general solution of x + x = 2x + 2x is x = np or x = nq 3 + 6 for n Z then p : q =

Options

  1. A1:1
  2. B1:2
  3. C2:3
  4. D2:1

Correct answer

A. 1:1

Step-by-step solution

Given equation: x + x = 2x + 2x Dividing both sides by 2 , we get: 1 2 x + 1 2 x = 1 2 2x + 1 2 2x (x - 4 ) = (2x - 4 ) The general solution for = is = 2n , where n Z . Therefore, 2x - 4 = 2n (x - 4 ) Taking the positive sign: 2x - 4 = 2n + x - 4 x = 2n Comparing this with x = np , we get p = 2 . Taking the negative sign: 2x - 4 = 2n - x + 4 3x = 2n + 2 x = 2n 3 + 6 Comparing this with x = nq 3 + 6 , we get q = 2 . Thus, the ratio p : q = 2 : 2 = 1 : 1 .

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