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AP EAMCET202316 May 2023Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

^4 8 + ^4 3 8 + ^4 5 8 + ^4 7 8 =

Options

  1. A1 4
  2. B3 8
  3. C3 2
  4. D3 4

Correct answer

C. 3 2

Step-by-step solution

^4 ( 8 )+ ^4 ( 3 8 )+ ^4 ( 5 8 )+ ^4 ( 7 8 )= ^4 ( 8 )+ ^4 ( 3 8 )+ ^4 ( - 3 8 )+ ^4 ( - 8 )= ^4 ( 8 )+ ^4 ( 3 8 )+ ^4 ( 3 8 )+ ^4 ( 8 )=2 [ ^4 ( 8 )+ ^4 ( 3 8 ) ]=2 [ ( 1- ( 4 ) 2 )^2+ ( 1- ( 3 4 ) 2 )^2 ]= [ ( 1- 1 2 2 )^2+ ( 1+ 1 2 2 )^2 ]= 2 4 [ (1- 1 2 )^2+ (1+ 1 2 )^2 ]= 3 2 ^4 8 + ^4 3 8 + ^4 5 8 + ^4 7 8 = 3 2 .

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