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

Question

Let θ ∈(0, (π/2)). If the system of linear equations (1+ cos 2 θ) x+ sin 2 θ y+4 sin 3 θ z=0 cos 2 θ x+(1+ sin 2 θ) y+4 sin 3 θ z=0 cos 2 θ x+ sin 2 θ y+(1+4 sin 3 θ) z=0 has a non-trivial solution, then the value of θ is : (A) (4 π/9) (B) (7 π/18) (C) (π/18) (D) (5 π/18)

Tardigrade Admin · Accepted Answer

Case-I | 1+ cos 2 θ sin 2 θ 4 sin 3 θ cos 2 θ 1+ sin 2 θ 4 sin 3 θ cos 2 θ sin 2 θ 1+4 sin 3 θ |=0 C 1 arrow C 1+ C 2 |2 sin 2 θ 4 sin 3 θ 2 1+ sin 2 θ 4 sin 3 θ 1 sin 2 θ 1+4 sin 3 θ|=0 R 1 arrow R 1- R 2, R 2 arrow R 2- R 3 |0 -1 0 1 1 -1 1 sin 2 θ 1+4 sin 3 θ |=0 or 4 sin 3 θ=-2 sin 3 θ=-(1/2) θ=(7 π/18)

Q. Let $θ \in (0, \frac{π}{2})$ . If the system of linear equations
$(1 + cos^{2} θ) x + sin^{2} θ y + 4 sin 3 θ z = 0$
$cos^{2} θ x + (1 + sin^{2} θ) y + 4 sin 3 θ z = 0$
$cos^{2} θ x + sin^{2} θ y + (1 + 4 sin 3 θ) z = 0$
has a non-trivial solution, then the value of $θ$ is :

$\frac{4 π}{9}$

$\frac{7 π}{18}$

$\frac{π}{18}$

$\frac{5 π}{18}$

Q. Let θ∈(0,2π​). 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 :

94π​

187π​

18π​

185π​

Q. Let $θ \in (0, \frac{π}{2})$ . If the system of linear equations
$(1 + cos^{2} θ) x + sin^{2} θ y + 4 sin 3 θ z = 0$
$cos^{2} θ x + (1 + sin^{2} θ) y + 4 sin 3 θ z = 0$
$cos^{2} θ x + sin^{2} θ y + (1 + 4 sin 3 θ) z = 0$
has a non-trivial solution, then the value of $θ$ is :

$\frac{4 π}{9}$

$\frac{7 π}{18}$

$\frac{π}{18}$

$\frac{5 π}{18}$