Consider the system of linear equations in `x , ya n dz :` `""(sin3theta)x-y+z=0(cos2theta)x+4y+3z=0` `3x+7y+7z=0` Which of the following can be the value of `theta` for which the system has a non-trivial solution `npi+(-1)^npi/6,AAn in Z` `npi+(-1)^npi/3,AAn in Z` `npi+(-1)^npi/9,AAn in Z` none of these

Explanation

As given equations has a non-trivial solution,

`:. |[sin3theta,-1,1],[cos2theta,4,3],[2,7,7]| = 0`

`=>sin3theta(28-21)-cos2theta(-7-7) +2(-3-4) = 0`

`=>7sin3theta + 14cos2theta -14 =0`

`=>sin3theta +2cos2theta -2 = 0`

`=>3sintheta - 4sin^3theta +2- 4sin^2theta -2 =0`

`=>-sintheta(4sin^2theta + 4sintheta -3) = 0`

`=>sintheta(4sin^2theta + 6sintheta - 2sintheta -3) = 0`

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