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AP EAMCET2005MathematicsTrigonometric Equations

If 2 x=( 2 +1) ( x- 1 2 ), x 1 2 , then x

Options

  1. A2 n 3 : n Z
  2. B2 n 6 : n Z
  3. C2 n 2 : n Z
  4. D2 n 4 : n Z

Correct answer

D. 2 n 4 : n Z

Step-by-step solution

aligned & 2 x=( 2 +1) ( x- 1 2 ) & 2 x= 2 x-1+ x- 1 2 & 1+ 2 x= x( 2 +1)- 1 2 & 2 ^2 x- x( 2 +1)+ 1 2 =0 & x= ( 2 +1) ( 2 +1)^2- 8 2 2(2) & = ( 2 +1) 3+2 2 -4 2 4 & = ( 2 +1) ( 2 -1)^2 4 & = 2 +1 ( 2 -1) 4 & aligned on taking + ve sign aligned x & = 2 +1+ 2 -1 4 = 2 2 4 = 1 2 x & =2 n 4 n Z aligned

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