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The system of equations (sin3θ)xy+z=0, (cos2θ)x+4y+3z=0, 2x+7y+7z=0 has a non-trivial solution if

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a
sin3θ+2cos2θ=2
b
sin3θ−2cos2θ=2
c
sin3θ−2cos2θ=1
d
sin3θ+2cos2θ=1

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detailed solution

Correct option is A

Given equations have a non-zero solution⇒sin3θ-11cos2θ43277=0⇒sin3θ28−21+17cos2θ−6+17cos2θ−8=0⇒7sin3θ+14cos2θ−14=0⇒sin3θ+2cos2θ=2


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If the system of equations xy+z=0, kxy+3z=0, x+2y+3z=0 has non trivial solution then K=

 

 


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