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AP EAMCET201921 Apr 2019Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

aligned & ^4 8 + ^4 2 8 + ^4 3 8 + ^4 4 8 & + ^4 5 8 + ^4 6 8 + ^4 7 8 = aligned

Options

  1. A3 2
  2. B5 2
  3. C3
  4. D7 2

Correct answer

C. 3

Step-by-step solution

aligned ^4 8 + ^4 2 8 + & ^4 3 8 + ^4 4 8 & + ^4 5 8 + ^4 6 8 + ^4 7 8 aligned aligned & = [ ^4 8 + ^4 3 8 + ^4 5 8 + ^4 7 8 ] & + [ ^4 2 8 + ^4 4 8 + ^4 6 8 ] & = [ ^4 8 + ^4 3 8 + ^4 ( 2 - 5 8 ) . & .+ ^4 ( 2 - 7 8 ) ]+ [ ^4 4 + ^4 2 + ^4 3 4 ] & = [ ^4 8 + ^4 3 8 + ^4 (- 8 )+ ^4 ( -3 8 ) ] & + [ ^4 4 + ^4 2 + ^4 ( 2 + 4 ) ] & = [ ^4 8 + ^4 3 8 + ^4 8 + ^4 3 8 ] & + [ ^4 4 + ^4 2 + ^4 4 ] & = [ ( ^4 8 + ^4 8 )+ ( ^4 3 8 + ^4 3 8 ) ] & + [ ( 1 2 )^4+(1)^4+ ( 1 2 )^4 ] & = [ (1-2 ^2 8 ^2 8 )+ (1-2 ^2 3 8 ^2 3 8 ) ]

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