If  x1,x2,x3,x4are roots of the equation x4−x3sin2β+x2cos2β−xcosβ−sinβ=0then Tan−1x1+Tan−1x2+Tan−1x3+Tan−1x4=

from the given equation∑x1=sin2β;∑x1x2=cos2β;∑x1x2x3=cosβ;and x1x2x3x4=−sinβ∴tan−1(x1)+tan−1x2+tan−1x3+tan−1x4=tan−1∑x1−∑x1x2x31−∑x1x2+x1x2x3x4=tan−1sin2β-cosβ1-cos2β-sinβ=tan−12sinβcosβ-cosβ2sin2β-sinβ=tan−1cosβ2sinβ-1sinβ2sinβ-1=tan−1cotβ=tan−1tanπ2-β=π2-β