If the the equation `a sin x + cos 2x=2a-7` possesses a solution, then find the values of a.

Explanation

The given equation can be written as
`a sin x+(1-2 sin^(2) x)=2a-7`
or `2 sin^(2) x-a sin x +2a-8=0`
or `sin x= (a pm sqrt(a^(2)-8(2a-8)))/4=(a pm (a-8))/4`
`=((a-4))/2 " "( :' sin x=2" is not possible")`
Equation has solution if `-1 le (a-4)//2 le 1`. Thus,
`-2 le (a-4) le 2`
`2 le a le 6`