# 41) The number of values of $\theta \in(0, \pi)$ for which the system of linear equations $\begin{array}{l} x+3 y+7 z=0 \\ -x+4 y+7 z=0 \\ (\sin 3 \theta) x+(\cos 2 \theta) y+2 z=0 \end{array}$ has a non-trivial solution, is [JEE (Main)-2019] (1) Four (2) One (3) Three (4) Two

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41) The number of values of $\theta \in(0, \pi)$ for which the system of linear equations $\begin{array}{l} x+3 y+7 z=0 \\ -x+4 y+7 z=0 \\ (\sin 3 \theta) x+(\cos 2 \theta) y+2 z=0 \end{array}$ has a non-trivial solution, is [JEE (Main)-2019] (1) Four (2) One (3) Three (4) Two

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Answer: (4) Two

Let's expand along the row 1

⇒ 1 ( 8 − 7 cos 2 θ ) − 3 ( − 2 − 7 sin 3 θ ) + 7 ( − cos 2 θ − 4 sin 3 θ ) = 0

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