Let θ (0,(π)/2). If the system of linear equations (1 + cos ²θ)x + sin ²θ y + 4 sin 3 θ z = 0 cos ²θ x + (1 + sin ²θ)y + 4 sin 3 θ z = 0 cos ²θ x + sin ²θ y + (1 + 4 sin 3 θ)z = 0 has a non-trivial solution, then the value of θ is:

Matrices and Determinants: JEE Main 2021 Mathematics question

JEE Main 2021 · 26 Aug, Morning shift · Q4597

JEE Main 202126 Aug, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\theta \in \left( {0,{\pi \over 2}} \right)

. If the system of linear equations

(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0

{\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0

{\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0

has a non-trivial solution, then the value of

\theta

is :

JEE Main 2021 · 26 Aug, Morning shift · Q4597

JEE Main 202126 Aug, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\theta \in \left( {0,{\pi \over 2}} \right)

. If the system of linear equations

(1 + {\cos ^2}\theta )x + {\sin ^2}\theta y + 4\sin 3\,\theta z = 0

{\cos ^2}\theta x + (1 + {\sin ^2}\theta )y + 4\sin 3\,\theta z = 0

{\cos ^2}\theta x + {\sin ^2}\theta y + (1 + 4\sin 3\,\theta )z = 0

has a non-trivial solution, then the value of

\theta

is :