The number of values of θ ∈ 0 , π for which the system of linear equations x + 3 y + 7 z = 0 - x + 4 y + 7 z = 0 sin ⁡ 3 θ x + cos ⁡ 2 θ y + 2 z = 0 has a non-trivial solution, is:

Step-by-step solution

For non-trivial solutions 1 3 7 - 1 4 7 s i n 3 θ c o s 2 θ 2 = 0 ⇒ 4 s i n 3 θ + 4 s i n 2 θ - 3 s i n θ = 0 ⇒ s i n θ = 0 or s i n θ = 1 2 or s i n θ = - 3 2 Since θ ∈ 0 ,   π ⇒ θ = π 6 and 5 π 6 will satisfy the equation because sin θ = - 3 2 is not possible as range of sin θ is - 1 , 1 ⇒ Number of θ ' s = 2