The equation `asinx+Cos2x=2a-7` possesses a solution if

Explanation

Given equation is,

`asinx + cos2x = 2a-7`

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

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

`=> sinx = (-(-a)+-sqrtD)/(2(2))`

Here, `D = (-a)^2-4(2)(2a-8)`

`=> D = a^2-16a+64 = (a-8)^2`

`:. sinx = (a+-(a-8))/4`

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