Let S be the set of all α∈R such that the equation, cos 2x + αsin x = 2α - 7 has a solution. Then S is equal to:

Correct option is A. [2,6]
Given, cos 2x + αsin x = 2α - 7
1 - 2sin²x + αsin x = 2α - 7
2sin²x - αsin x + 2α - 8 = 0
2(sin²x - 4) - α(sin x - 2) = 0
2(sin x - 2)(sin x + 2) - α(sin x - 2) = 0
(sin x - 2)(2sin x + 4 - α) = 0
∴ 2sin x + 4 - α = 0 (since sin x - 2 = 0 is not possible)
⇒ sin x = (α - 4)/2
As we know -1 ≤ sin x ≤ 1
∴ -1 ≤ (α - 4)/2 ≤ 1
⇒ -2 ≤ α - 4 ≤ 2
⇒ 2 ≤ α ≤ 6
∴ α ∈ [2,6]
Hence correct option is (A)