If the equation `asinx+cos2x=2a-7` possesses a solution, then find the value of `adot`

Options

A. `a in [2,4]`
B. `a in [2,6]`
C. `a in [2,8]`
D. `a in [2,10]`

Answer

B

Explanation

`asinx +cos2x = 2a-7`

`=>asinx+1-2sin^2x = 2a-7`

`=>2sin^2x - asinx +2a-8 = 0`

`=>sinx = (a+-sqrt(a^2 - 4(2)(2a-7)))/4`

`=>sinx = (a+-sqrt(a^2 - 16a+64))/4`

`=>sinx = (a+-sqrt((a-8)^2))/4`

`=>sinx = (a+a-8)/4 and sin x = (a-a+8)/4`

`=>sinx = (a-4)/2 and sinx = 2`

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