If cos ⁡ 2 x + 2 cos ⁡ x = 1 , then sin 2 ⁡ x 2 - cos 2 ⁡ x is equal to

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Correct answer: 1

cos ⁡ 2 x + 2 cos ⁡ x = 1 2 cos 2 ⁡ x - 1 + 2 cos ⁡ x = 1 cos 2 ⁡ x + cos ⁡ x - 1 = 0 cos ⁡ x = - 1 ± 5 2 cos ⁡ x = 5 - 1 2 ⇒ cos 2 ⁡ x = 5 + 1 - 2 5 4 = 3 - 5 2 sin 2 ⁡ x 2 - cos 2 ⁡ x = 1 - cos 2 ⁡ x 2 - cos 2 ⁡ x = 1 - 3 - 5 2 2 - 3 - 5 2 = 2 - 3 + 5 2 4 - 3 + 5 2 = 5 - 1 2 5 + 1 2 = 4 4 = 1

If cos ⁡ 2 x + 2 cos ⁡ x = 1 , then sin 2 ⁡ x 2 - cos 2 ⁡ x is equal to

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