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COMEDK2021MathematicsTrigonometric Equations

If 2 x=4 x , then x is equal to

Options

  1. An 2 4 , n Z
  2. Bno value
  3. Cn +(-1)^ n 4 , n Z
  4. D2 n 2 , n Z

Correct answer

D. 2 n 2 , n Z

Step-by-step solution

Given the equation 2x = 4 x . Using the double angle identity 2x = 2 x x , the equation becomes: 2 x x = 4 x Rearranging the terms: 2 x x - 4 x = 0 2 x ( x - 2) = 0 This implies either x = 0 or x - 2 = 0 . For x = 0 , the general solution is x = (2n + 1) 2 = n + 2 , where n Z . For x = 2 , there is no real solution since the range of x is [-1, 1] . Comparing the obtained solution x = n + 2 with the given options, we check the values generated by 2n 2 . For n + 2 , the values are , - 2 , 2 , 3 2 , . For 2n 2 , the v

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