If the pair of lines represented by the combined equation 2x2+4xy+y2=0 makes angles θ1,θ2with x−axis then cosθ1−θ2=

If θ1,θ2 are the inclination of the lines represented by the combined equation 2x2+4xy+y2=0 then θ1−θ2 is the angle between those two lines. If θ is acute angle between pair of lines represented by the equation ax2+2hxy+by2=0 then cosθ=a+b(a−b)2+(2h)2For the equation 2x2+4xy+y2=0,a=2,h=2,b=1 ,   Hence, cosθ1−θ2=31+16=317Therefore, the required value is cosθ1−θ2=317