Let S be the set of all α   ∈   R such that the equation, c o s 2 x + α s i n x…

Let S be the set of all α ∈ R such that the equation, cos2x+αsinx=2α-7 has a solution. Then S is equal to:
  1. 3, 7
  2. 2, 6
  3. 1, 4
  4. R

Solution

The given equation can be written as:
1-2sin2⁡x+ α sinx=2α-7
⇒2sin2⁡x-αsin⁡x+2α-8=0
⇒sinx=α-4 2,  2 sinx ≠2
For at least one solution
-1≤α-42 ≤1
⇒α∈[2,6]

Asked in: JEE Main 2019 (12 Apr Shift 2)

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