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AP EAMCET2012MathematicsTrigonometric Ratios & Identities

If x+ (x+ 3 )+ (x+ 2 3 )=3 then 3 x is equal to

Options

  1. A3
  2. B2
  3. C1
  4. D0

Correct answer

C. 1

Step-by-step solution

aligned & LHS = x+ (x+ 3 )+ (x+ 2 3 ) & = x+ x+ 3 1- 3 x + x- 3 1+ 3 x & = x+ [ array c ( x+ 3 )(1+ 3 x) +( x- 3 )(1- 3 x) array ] 1-3 ^2 x & = [ array c x (1-3 ^2 x )+ x+ 3 + 3 ^2 x+3 x+ x- 3 - 3 ^2 x+3 x array ] 1-3 ^2 x & x (1-3 ^2 x )+8 x 1-3 ^2 x =3 (given) & x (1-3 ^2 x )+8 x & =3 (1-3 ^2 x ) & aligned aligned & x (9-3 ^2 x )=3 (1-3 ^2 x ) & x (3- ^2 x )=1-3 ^2 x & 3 x- ^3 x 1-3 ^2 x =1 & 3 x=1 aligned

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