If Δ₁|x sinθ cosθ;... | Determinants

JEE MAIN_2019_

10-04-2019-S-1

Question

If $\Delta_1\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ and $\Delta_2\left|\begin{array}{ccc}x & \sin 2 \theta & \cos \theta \\ -\sin 2 \theta & -x & 1 \\ \cos 2 \theta & 1 & x\end{array}\right|, x \neq 0 ;$ then for all $\theta \in\left(0, \frac{\pi}{2}\right):$

Select the correct option:

$\Delta 1+\Delta 2=-2 x^3$

$\Delta 1-\Delta 2=-2 x^3$

$\Delta 1+\Delta 2=-2\left(x^3+x-1\right)$

$\Delta 1-\Delta 2=x(\cos 2 \theta-\cos 4 \theta)$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution