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2+ 2+ 2+2 8 where [- 8 , 8 ] is equal to

Options

  1. A2
  2. B2
  3. C2
  4. D2

Correct answer

D. 2

Step-by-step solution

Let the given expression be E = 2+ 2+ 2+2 8 . Using the trigonometric identity 1 + 2A = 2 ^2 A , we have 2 + 2 8 = 2(1 + 8 ) = 2(2 ^2 4 ) = 4 ^2 4 . Since [- 8 , 8 ] , 4 [- 2 , 2 ] , so 4 0 . Thus, 2+2 8 = 4 ^2 4 = 2 4 . Substituting this into the expression, E = 2+ 2+2 4 . Applying the same identity again, 2 + 2 4 = 2(1 + 4 ) = 2(2 ^2 2 ) = 4 ^2 2 . Since 2 [- 4 , 4 ] , 2 0 . Thus, 2+2 4 = 2 2 . Substituting this into the expression, E = 2+2 2 . Applying the identity once more, 2 + 2 2 = 2(1 + 2 ) = 2(2 ^2 ) = 4 ^

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