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

 

  • Option 1)

    R

  • Option 2)

    [1,4]

  • Option 3)

    [3,7]

  • Option 4)

    [2,6]

 

Answers (1)
V Vakul

\cos 2x+\alpha \sin x=2\alpha -7

=> 1-2sin^{2}x +\alpha sinx=2\alpha -7

=> 2sin^{2}x -\alpha sinx+2\alpha -8=0

=> sinx=\frac{\alpha-4}{2},2 (sinx\neq2)

For atleast one solution,

-1\leq \frac{\alpha -4}{2}\leq 1

\alpha \epsilon [2,6]


Option 1)

R

Option 2)

[1,4]

Option 3)

[3,7]

Option 4)

[2,6]

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