The maximum value of f(x) = left|begin{array} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $f(x) = \left|\begin{array}{ccc} \sin^{2} x & 1+\cos^{2} x & \cos 2x \ 1+\sin^{2} x & \cos^{2} x & \cos 2x \ \sin^{2} x & \cos^{2} x & \si

Vedclass · Accepted Answer

$\sqrt{5}$

Vedclass · Answer

(C) Given $f(x) = \left|\begin{array}{ccc} \sin^{2} x & 1+\cos^{2} x & \cos 2x \ 1+\sin^{2} x & \cos^{2} x & \cos 2x \ \sin^{2} x & \cos^{2} x & \sin 2x \end{array}ight|$.Apply the column operation $C_{1} ightarrow C_{1} + C_{2}$:$f(x) = \left|\begin{array}{ccc} \sin^{2} x + 1 + \cos^{2} x & 1+\cos^{2} x & \cos 2x \ 1+\sin^{2} x + \cos^{2} x & \cos^{2} x & \cos 2x \ \sin^{2} x + \cos^{2} x & \cos^{2} x & \sin 2x \end{array}ight| = \left|\begin{array}{ccc} 2 & 1+\cos^{2} x & \cos 2x \ 2 & \cos^{2} x & \cos 2x \ 1 & \cos^{2} x & \sin 2x \end{array}ight|$.Apply the row operation $R_{1} ightarrow R_{1} - R_{2}$:$f(x) = \left|\begin{array}{ccc} 0 & 1 & 0 \ 2 & \cos^{2} x & \cos 2x \ 1 & \cos^{2} x & \sin 2x \end{array}ight|$.Expanding along $R_{1}$:$f(x) = -1 	imes (2 \sin 2x - \cos 2x) = \cos 2x - 2 \sin 2x$.The maximum value of $a \cos 	heta + b \sin 	heta$ is $\sqrt{a^{2} + b^{2}}$.Here $a = 1$ and $b = -2$.So,$f(x)_{\max} = \sqrt{1^{2} + (-2)^{2}} = \sqrt{1+4} = \sqrt{5}$.

List-$I$	List-$II$
a) $A$ matrix which is not a square matrix	i) Symmetric matrix
b) $A$ square matrix $A' = A$	ii) Null matrix
c) The diagonal elements of a diagonal matrix are same	iii) Rectangular matrix
d) $A$ matrix which is both symmetric and skew symmetric	iv) Scalar matrix

The maximum value of $f(x) = \left|\begin{array}{ccc} \sin^{2} x & 1+\cos^{2} x & \cos 2x \\ 1+\sin^{2} x & \cos^{2} x & \cos 2x \\ \sin^{2} x & \cos^{2} x & \sin 2x \end{array}\right|, x \in R$ is:

Similar Questions

The number of $3 \times 3$ non-singular matrices,with four entries as $1$ and all other entries as $0$,is

Let $P$ be an $m \times m$ matrix such that $P^2=P$. Then,$(I+P)^n$ equals

If $A$ is a skew-symmetric matrix of order $3$ and $X$ is another matrix of the same order,then $|XA + AX^T|$ is (where $|P|$ denotes the determinant of matrix $P$).

If $A = \begin{bmatrix} 1 & a & 3 \\ b & 2 & c \\ 3 & d & 4 \end{bmatrix}$ is a symmetric matrix and $B = \begin{bmatrix} 0 & 5 & b \\ -5 & 0 & -7 \\ 6 & c & 0 \end{bmatrix}$ is a skew-symmetric matrix, then $AB = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module