Number of integral values of `a` for which the equation `cos^2x-sinx+a=0` has roots when `x in (0,pi/2)` is____________

Explanation

`cos^2x-sinx+a=0`

`1-sin^2x-sinx+a=0`

`sin^2x+sinx-a-1=0`

`(-1)^2-4(1)(-a-x)>=0`

`1+4(a+1)>=0`

`a>=-5/4`

`0<-a-1<1`

`1<-a<2`

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