Let m and M be respectively the minimum and maximum value values of $|\begin{matrix} \cos^{2} x & 1 + \sin^{2} x & \sin 2 x \\ 1 + \cos^{2} x & \sin^{2} x & \sin 2 x \\ \cos^{2} x & \sin^{2} x & 1 + \sin 2 x \end{matrix}|$ Then the ordered pair (m, M) is equal to:

Question

Let m and M be respectively the minimum and maximum value values of cos 2 x 1 + sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x sin 2 x 1 + sin 2 x Then the ordered pair (m, M) is equal to:

TestHub · Accepted Answer

D = cos 2 x 1 + sin 2 x sin 2 x 1 + cos 2 x sin 2 x sin 2 x cos 2 x sin 2 x 1 + sin 2 x C 1 → C 1 + C 2 D = 2 1 + sin 2 x sin 2 x 2 sin 2 x sin 2 x 1 sin 2 x 1 + sin 2 x R 1 → R 1 - 2 R 3 and R 2 → R 2 - 2 R 3 D = 0 cos 2 x - ( 2 + sin 2 x ) 0 - sin 2 x - ( 2 + sin 2 x ) 1 sin 2 x 1 + sin 2 x ⇒ D = - 2 - sin 2 x As range of sin 2 x ∈ - 1 , 1 , thus m = - 3 , M = - 1

Mathematics - Determinant Question with Solution | TestHub

Options:

Doubts & Discussion