1.

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

Answer» `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`
We know, `sinx !=2`,
`:. sinx = (a-4)/2`
`:. -1 le (a-4)/2 le 1`
`=>2 le a le 6`
`:. a in [2,6]`, which is required solution.


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