Crey | Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α? 2α = 2nπ ± π/2 + π/2, 2α = 2nπ ± π/2 + π/4, 2α = 2nπ ± π/4 + π/4, 2α = 2nπ ± π/4 + π/2

Question

Let, α and β be real. Find the set of all values of β for which the system of equation βx + sin α*y + cosα*z = 0, x + cosα * y + sinα * z = 0 , -x + sinα*y – cosα * z = 0 has a non-trivial solution. For β = 1 what are all values of α?

Options :

2α = 2nπ ± π/2 + π/2
2α = 2nπ ± π/2 + π/4
2α = 2nπ ± π/4 + π/4
2α = 2nπ ± π/4 + π/2

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