$\Delta=\left|\begin{array}{ccc} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \end{array}\right|$

(A) $\Delta=2\left(1-\cos ^2 x\right)$
(B) $\Delta=2\left(2-\sin ^2 x\right)$
(C) Minimum value of $\Delta$ is 2
(D) Maximum value of $\Delta$ is 4

Choose the correct answer from the options given below:

(B), (C) and (D) only

The correct answer is Option (4) → (B), (C) and (D) only

$\Delta=\left|\begin{array}{ccc} 1 & \cos x & 1 \\ -\cos x & 1 & \cos x \\ -1 & -\cos x & 1 \end{array}\right|$

$=1+\cos^2x+\cos x(-\cos x+\cos x)+1+\cos^2x$

$=2(1+\cos^2x)$

$=2(2-\sin^2x)=Δ$

$0≤\cos^2x≤1$

$1≤1+\cos^2x≤2$

$2≤2(1+\cos^2x)≤4$

min value = 2

max value = 4

B, C, D only correct