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If the system of linear equations (sin3θ)xy+z=0,   (cos2θ)x+4y+3z=0, 2x+7y+7z=0 has a non-trivial solution, then the values of  θare

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a
nπ,  nπ+(−1)nπ3
b
nπ,  nπ+(−1)nπ6
c
nπ,  nπ+(−1)nπ2
d
nπ,  nπ+(−1)nπ4

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detailed solution

Correct option is B

Given equations has non-trivial solution⇒sin3θ-11cos2θ43277=0⇒sin3θ+2cos2θ−2=0⇒3sinθ−4sin2θ−4sin3θ=0⇒sinθ=0  (or)  sinθ=12⇒θ=nπ  (or)   θ=nπ+(−1)nπ6,  n∈z


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