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

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 sin 2 18 ∘ - 4 + 1 4 sin 2 54 ∘ - 4 + 1 = 36 4 sin 2 18 ∘ - 3 4 sin 2 54 ∘ - 3 = 36 5 - 1 2 4 - 3 5 + 1 2 4 - 3 = 36 6 - 2 5 - 12 4 6 + 2 5 - 12 4 = - 36 2 5 2 - 36 16 = 36 Hence this is the correct option.