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Question

Let S be the set of all αR such that the equation, cos2x+αsinx=2α7 has a solution. Then S is equal to: 


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

Solution

The correct option is B [2,6]
cos2x+αsinx=2α7
12sin2x+αsinx=2α72sin2xαsinx+2α8=0sinx=α±α28(2α8)4sinx=α42,2
As sinx=2 is not possible so,
sinx=α421α4212α6

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