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KCET2010MathematicsTrigonometric Equations

The general solution of 1+ ² x=3 x x, x 1 2 , is

Options

  1. A2 n + 4 , n Z
  2. B2 n - 4 , n Z
  3. Cn - 4 , n Z
  4. Dn + 4 , n Z

Correct answer

D. n + 4 , n Z

Step-by-step solution

1+ ² x=3 x x, x 1 2 Divided by ² x on both sides, gathered 1 ² x + ² x ² x =3 x x x x ² x + ² x =3 x 1+ ² x + ² x =3 x 2 ² x -3 x +1=0 2 ² x -2 x - x +1=0 2 x ( x -1)-1( x -1)=0 ( x -1)(2 x -1)=0 x =1, 1 2 We take, x =1 ( x 1 2 ) x = tan ( / 4) gathered x = n + / 4, n Z

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