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

Step-by-step solution

The given equation can be written as: 1 - 2 sin 2 ⁡ x + α s i n x = 2 α - 7 ⇒ 2 sin 2 ⁡ x - α sin ⁡ x + 2 α - 8 = 0 ⇒ s i n x = α - 4 2 , 2 s i n x ≠ 2 For at least one solution - 1 ≤ α - 4 2 ≤ 1 ⇒ α ∈ [ 2,6 ]