The number of values of α in - 10 π , 10 π for which the equations sin ⁡ α x - cos ⁡ α y + 3 z = 0 , cos ⁡ α x + sin ⁡ α y - 2 z = 0 and 2 x + 3 y + cos ⁡ α z = 0 have nontrivial solution is

Step-by-step solution

For non-trivial solution ∆ = 0 sin ⁡ α - cos ⁡ α 3 cos ⁡ α sin ⁡ α - 2 2 3 cos ⁡ α = 0 ⇒ sin ⁡ α sin ⁡ α cos ⁡ α + 6 + cos ⁡ α cos 2 ⁡ α + 4 + 3 3 cos ⁡ α - 2 sin ⁡ α = 0 ⇒ sin 2 ⁡ α cos ⁡ α + 6 sin ⁡ α + cos 3 ⁡ α + 4 cos ⁡ α + 9 cos ⁡ α - 6 sin ⁡ α = 0 ⇒ 14 cos ⁡ α = 0 &#86