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

Answer

1

Explanation

`1-sin^(2) x-sin x+a=0`
`rArr sin^(2)x+sin x=(a+1)`
For `x in (0, pi//2)`, the range of `sin^(2) x+sin x` is `(0, 2)`.
`rArr 0 lt (a+1) lt 2`
`rArr a in (-1, 1)`