Given pair of lines is (x2+y2)cos2θ=(xcosθ+ysinθ)2 ⇒ (x2+y2)cos2θ=x2cos2θ+y2sin2θ+2xysinθcosθ ⇒ y2(cos2θ−sin2θ)−2xysinθcosθ=0 ∵ Pair of lines are perpendicular to each other. ∴ Coefficient of x2+ Coefficient of y2=0 ∴ 0+cos2θ−sin2θ=0 ⇒ tan2θ=1 ⇒ tanθ=±1⇒θ=