If there exists at least one real x which satisfies both the equatios `x^(2)+2xsiny+1=0`, where `yin(0,pi//2),andax^(2)+x+1=0`, then the value of `a+siny` is ______.

Answer

1.5

Explanation

For equation `x^(2)+2xsiny+1=0`
`D=4sin^(2)y-4lt0`
Thus, equations have both roots common.
`implies(1)/(a)=(2siny)/(1)=(1)/(1)`
`impliesa=1,siny=(1)/(2)`
`:.a+siny=1.5`