Question

# 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:

A
R
B
[2,6]
C
[1,4]
D
[3,7]

Solution

## The correct option is B [2,6]cos2x+αsinx=2α−7 ⇒1−2sin2x+αsinx=2α−7⇒2sin2x−αsinx+2α−8=0⇒sinx=α±√α2−8(2α−8)4⇒sinx=α−42,2 As sinx=2 is not possible so, sinx=α−42⇒−1≤α−42≤1⇒2≤α≤6

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