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The value of 36 4 cos 2 9 ∘ - 1 4 cos 2 27 ∘ - 1 4 cos 2 81 ∘ - 1 4 cos 2 243 ∘ - 1 is

Options

  1. A54
  2. B18
  3. C27
  4. D36

Correct answer

D. 36

Step-by-step solution

We need to find the value of 36 4   cos 2   9 ∘ - 1   4   cos 2   27 ∘ - 1   4   cos 2   81 ∘ - 1   4   cos 2   243 ∘ - 1   = 36 4   cos 2 9 ∘ - 1   4   sin 2 9 ∘ - 1   4   cos 2 27 ∘ - 1 4   sin 2 27 ∘ - 1 = 36 4 2 cos 9 ∘ sin 9 ° 2 - 4 cos 2 9 ° - 4 sin 2 9 ° + 1   4 2 sin 27 ∘ cos 9 ° 2 - 4 cos 2 27 ° - 4 sin 2 27 ° + 1 = 36 4 &#1

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