If the system of linear equations $$sin$$ $$3$$θx−$$y+z=0$$, $$cos2$$θ$$x+4y+3z=0$$ , $$2x+7y+7z=0$$ has a $$non-trivial$$ solution then the values of θ are

Question

If the system of linear equations $$sin$$ $$3$$θx−$$y+z=0$$, $$cos2$$θ$$x+4y+3z=0$$ ,  $$2x+7y+7z=0$$ has a $$non-trivial$$ solution then the values of  θ are

Infinity Learn · Accepted Answer

Given equations have non zero solution  ⇒$$sin$$⁡$$3$$θ−$$11cos$$⁡$$2$$θ$$43277=0$$⇒$$($$$$sin$$⁡$$3$$θ$$)(28$$−$$21)$$−$$($$$$cos$$⁡$$2$$θ$$)($$−$$7$$−$$7)+2($$−$$3$$−$$4)=0$$⇒$$sin$$⁡$$3$$θ$$+2cos$$⁡$$2$$θ−$$2=0$$⇒$$3sin$$⁡θ−$$4sin3$$⁡θ$$+21$$−$$2sin2$$⁡θ$$=2$$⇒$$3sin$$⁡θ−$$4sin2$$⁡θ−$$4sin3$$⁡θ$$=0$$⇒−$$sin$$⁡θ$$4sin2$$⁡θ$$+4sin$$⁡θ−$$3=0$$⇒$$sin$$⁡θ$$(2sin$$⁡θ$$+3)(2sin$$⁡θ−$$1)=0$$⇒$$sin$$⁡θ$$=0$$ or $$sin$$⁡θ$$=1/2$$⇒θ$$=n$$π or θ$$=n$$π$$+($$−$$1)n$$π$$/6$$,n∈Z

If the system of linear equations $(\sin 3 θ) x - y + z = 0, (\cos 2 θ) x + 4 y + 3 z = 0$ , $2 x + 7 y + 7 z = 0$ has a non-trivial solution then the values of $θ$ are

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If the system of linear equations sin 3θx−y+z=0, cos2θx+4y+3z=0 , 2x+7y+7z=0 has a non-trivial solution then the values of θ are

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If the system of linear equations $(\sin 3 θ) x - y + z = 0, (\cos 2 θ) x + 4 y + 3 z = 0$ , $2 x + 7 y + 7 z = 0$ has a non-trivial solution then the values of $θ$ are