The angle between the lines represented by cos θ ( cos θ + 1 ) x 2 - 2 cos θ + sin 2 θ x y + ( 1 - cos θ ) y 2 = 0 is

Step-by-step solution

We have the equation of pair of straight lines cos θ ( cos θ + 1 ) x 2 - 2 cos θ + sin 2 θ x y + 1 - cos θ y 2 = 0 So, angle between them is θ = tan - 1 2 cos θ + sin 2 θ 2 2 - cos θ cos θ + 1 1 - cos θ cos θ cos θ + 1 + 1 - cos θ = tan - 1 2 cos 2 θ + sin 4 θ 4 + cos θ · sin 2 θ - cos θ 1 - cos 2 θ cos 2 θ + 1 = tan - 1 2 cos 2 θ + sin 4 θ 4 + cos θ · sin 2 θ - cos θ sin 2 &#9