JEE PYQ: Matrices And Determinants Question 67
Question 67 - 2019 (10 Apr Shift 1)
If $\Delta_1 = \begin{vmatrix} x & \sin\theta & \cos\theta \ -\sin\theta & -x & 1 \ \cos\theta & 1 & x \end{vmatrix}$ and $\Delta_2 = \begin{vmatrix} x & \sin 2\theta & \cos 2\theta \ -\sin 2\theta & -x & 1 \ \cos 2\theta & 1 & x \end{vmatrix}$, $x \neq 0$;
then for all $\theta \in \left(0, \dfrac{\pi}{2}\right)$:
(1) $\Delta_1 - \Delta_2 = -2x^3$
(2) $\Delta_1 - \Delta_2 = x(\cos 2\theta - \cos 4\theta)$
(3) $\Delta_1 \times \Delta_2 = -2(x^3 + x - 1)$
(4) $\Delta_1 + \Delta_2 = -2x^3$
BETA
