The number of θ ∈ 0 , 4 π for which the system of linear equations 3 sin 3 θ x - y + z = 2 3 cos 2 θ x + 4 y + 3 z = 3 6 x + 7 y + 7 z = 9 has no solution is

Step-by-step solution

The number of θ ∈ 0 , 4 π for which the system of linear equations 3 sin 3 θ x - y + z = 2 3 cos 2 θ x + 4 y + 3 z = 3 6 x + 7 y + 7 z = 9 has no solution is : We know that for the system of equation has no solution, D = 3 sin 3 θ - 1 1 3 cos 2 θ 4 3 6 7 7 = 0 ⇒ 21 sin 3 θ + 42 cos 2 θ - 42 = 0 ⇒ sin 3 θ + 2 cos 2 θ - 2 = 0 ⇒ 2 - 2 cos 2 θ = sin 3 θ ⇒ 4 sin 2 θ = 3 sin θ - 4 sin 3 θ ⇒ sin θ 4 sin &#95