Let \\theta\\in(0, \frac{\\pi}{2}). If the system of linear equations (1+\cos ^{2} \\theta) x+\sin ^{2} \\theta y+4 \sin 3 \\thetaz=0 \cos ^{2} \\thetax+(1+\sin ^{2} \\theta) y+4 \sin 3 \\thetaz =0 \cos ^{2} \\thetax+\sin ^{2} \\thetay+(1+4 \sin 3 \\theta) z=0 has a non-trivial solution, then the value of θ is [26 Aug 2021 Shift 1]

Matrices and Determinants Part 2

Section: Mathematics

Question : 39 of 100

Marks: +1, -0

Let θ∈(0,

). If the system of linear equations
(1+cos2θ)x+sin2θy+4‌sin‌3‌θ‌z=0
cos2θx+(1+sin2θ)y+4‌sin‌3‌θ‌z =0
cos2θx+sin2θy+(1+4‌sin‌3‌θ)z=0
has a non-trivial solution, then the value of θ is

[26 Aug 2021 Shift 1]

4π
9
7π
18
π
18
5π
18

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1+cos2θ	sin2θ	4‌sin‌3‌θ
cos2θ	1+sin2θ	4‌sin‌3‌θ
cos2θ	sin2θ	1+4‌sin‌3‌θ

1	0	−1
cos2θ	1+sin2θ	4‌sin‌3‌θ
cos2θ	sin2θ	1+4‌sin‌3‌θ

1	0	0
cos2θ	1+sin2θ	4‌sin‌3‌θ+cos2θ
cos2θ	sin2θ	1+4‌sin‌3‌θ+cos2θ