1.

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» `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`
`-1>a>-2`
Number of integral value of a =0.


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