The value of θ lying between -(π/4) (π/2) and 0 ≤ A ≤ (π/2) and satisfying the equation |1+ sin 2 A cos 2 A 2 sin 4 θ sin 2 A 1+ cos 2 A 2 sin 4 θ sin 2 A cos 2 A 1+2 sin 4 θ|=0 are -

Question

The value of θ lying between -(π/4) (π/2) and 0 ≤ A ≤ (π/2) and satisfying the equation |1+ sin 2 A cos 2 A 2 sin 4 θ sin 2 A 1+ cos 2 A 2 sin 4 θ sin 2 A cos 2 A 1+2 sin 4 θ|=0 are - (A) A =(π/4), θ=-(π/8) (B) A =(3 π/8)=θ (C) A =(π/5), θ=-(π/8) (D) A=(π/6), θ=(3 π/8)

Tardigrade Admin · Accepted Answer

|1+ sin 2 A cos 2 A 2 sin 4 θ sin 2 A 1+ cos 2 A 2 sin 4 θ sin 2 A cos 2 A 1+2 sin 4 θ|=0 C1 arrow C1+C2 ⇒|2 cos 2 A 2 sin 4 θ 2 1+ cos 2 A 2 sin 4 θ 1 cos 2 A 1+2 sin 4 θ|=0 R 1 arrow R 1- R 2 ⇒|0 -1 0 2 1+ cos 2 A 2 sin 4 θ 1 cos 2 A 1+2 sin 4 θ|=0 ⇒ 2(1+2 sin 4 θ)-2 sin 4 θ=0 ⇒ 1+ sin 4 θ=0 sin 4 θ=-1 4 θ=-(π/2) or 4 θ=(3 π/2) θ=-(π/8) or θ=(3 π/8) A ∈ R

Q. The value of $θ$ lying between $- \frac{π}{4} & \frac{π}{2}$ and $0 \leq A \leq \frac{π}{2}$ and satisfying the equation $∣ ∣ 1 + sin^{2} A sin^{2} A sin^{2} A cos^{2} A 1 + cos^{2} A cos^{2} A 2 sin 4 θ 2 sin 4 θ 1 + 2 sin 4 θ ∣ ∣ = 0$ are -

$A = \frac{π}{4}, θ = - \frac{π}{8}$

$A = \frac{3 π}{8} = θ$

$A = \frac{π}{5}, θ = - \frac{π}{8}$

$A = \frac{π}{6}, θ = \frac{3 π}{8}$

Q. The value of θ lying between −4π​&2π​ and 0≤A≤2π​ and satisfying the equation ∣∣​1+sin2Asin2Asin2A​cos2A1+cos2Acos2A​2sin4θ2sin4θ1+2sin4θ​∣∣​=0 are -

A=4π​,θ=−8π​

A=83π​=θ

A=5π​,θ=−8π​

A=6π​,θ=83π​

Q. The value of $θ$ lying between $- \frac{π}{4} & \frac{π}{2}$ and $0 \leq A \leq \frac{π}{2}$ and satisfying the equation $∣ ∣ 1 + sin^{2} A sin^{2} A sin^{2} A cos^{2} A 1 + cos^{2} A cos^{2} A 2 sin 4 θ 2 sin 4 θ 1 + 2 sin 4 θ ∣ ∣ = 0$ are -

$A = \frac{π}{4}, θ = - \frac{π}{8}$

$A = \frac{3 π}{8} = θ$

$A = \frac{π}{5}, θ = - \frac{π}{8}$

$A = \frac{π}{6}, θ = \frac{3 π}{8}$