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AP EAMCET201922 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

Let ( , ) and ( ) be such that (0 < < < < 2 ). For any (x R ) if ( (x+ )+ (x+ )+ (x+ )=0 , ) then ( ( - )= )

Options

  1. A(- 3 )
  2. B0
  3. C1
  4. D( 3 )

Correct answer

D. ( 3 )

Step-by-step solution

It is given that for any (x R ). ( (x+ )+ (x+ )+ (x+ )=0 ) Now, put (x=- - - ), (0 < < < < 2 ), we get ( aligned & ( + )+ ( + )+ ( + )=0 & 2 ( +2 + 2 ) ( - 2 ) + ( + )=0 (i) aligned ) Now, put (x= 2 - ), we get ( array ll & ( - )+ ( - )=0 & ( - )= ( - ) & 2 = + (ii) array ) From Eqs. (i) and (ii), we get ( array rc & ( + ) [ 1 2 ( - 2 )+1 ]=0 & ( - 2 )=- 1 2 & - 2 = 2 3 - = 3 array ) So, ( ( - )= 3 )

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