QJEEM19Maf8c3: JEE Main 2019 Mathematics - Class 12 JEEM19Maf8c3 Solution: If   A = [ 1 sin ⁡ θ 1 − sin ⁡ θ 1 sin ⁡ θ − 1 − sin…

Question

Verified Solution • 2025–26 Session moderate

If A =

[\begin{matrix} 1 & \sin θ & 1 \\ - \sin θ & 1 & \sin θ \\ - 1 & - \sin θ & 1 \end{matrix}]

;

then for all

θ

\in

(\frac{3 π}{4}, \frac{5 π}{4})

, det (A) lies in the interval :

Accepted Answer

| A | = | \begin{matrix} 1 & \sin θ & 1 \\ - \sin θ & 1 & \sin θ \\ - 1 & - \sin θ & 1 \end{matrix} |

= 2(1 + sin²

θ

)

θ

\in

(\frac{3 π}{4}, \frac{5 π}{4}) \Rightarrow \frac{1}{\sqrt{2}} < \sin θ < \frac{1}{\sqrt{2}}

\Rightarrow

0

\leq

sin²

θ

<

\frac{1}{2}

∴

| A | \in [2, 3)

QJEEM19Maf8c3: JEE Main 2019 Mathematics - Class 12 JEEM19Maf8c3 Solution: If&nbsp;&nbsp; A = [ 1 sin ⁡ θ 1 − sin ⁡ θ 1 sin ⁡ θ − 1 − sin…