If left| begin{array}{ccc} cos 2x & sin^2 x & | vedclass

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

Question

(C) To find the constant term $a_0$ in the expansion of the determinant,we set $x = 0$.Substituting $x = 0$ into the determinant:$\cos(2 	imes 0) = \

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(C) To find the constant term $a_0$ in the expansion of the determinant,we set $x = 0$.Substituting $x = 0$ into the determinant:$\cos(2 	imes 0) = \cos(0) = 1$$\sin^2(0) = 0$$\cos(4 	imes 0) = \cos(0) = 1$$\cos^2(0) = 1$The determinant becomes:$\Delta = \left| \begin{array}{ccc} 1 & 0 & 1 \ 0 & 1 & 1 \ 1 & 1 & 1 \end{array} ight|$Expanding along the first row:$\Delta = 1(1 	imes 1 - 1 	imes 1) - 0(0 	imes 1 - 1 	imes 1) + 1(0 	imes 1 - 1 	imes 1)$$\Delta = 1(0) - 0(-1) + 1(-1)$$\Delta = 0 + 0 - 1 = -1$Since the expansion is $a_0 + a_1 \sin x + a_2 \sin^2 x + \dots$,setting $x = 0$ gives $a_0 = -1$.

If $\left| \begin{array}{ccc} \cos 2x & \sin^2 x & \cos 4x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 4x & \cos^2 x & \cos 2x \end{array} \right| = a_0 + a_1 \sin x + a_2 \sin^2 x + \dots$,then $a_0$ is equal to:

Similar Questions

If $a+x=b+y=c+z+1,$ where $a, b, c, x, y, z$ are non-zero distinct real numbers,then $\left|\begin{array}{lll}x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c\end{array}\right|$ is equal to

The constant term in the expansion of $ \left|\begin{array}{ccc} 3x+1 & 2x-1 & x+2 \\ 5x-1 & 3x+2 & x+1 \\ 7x-2 & 3x+1 & 4x-1 \end{array}\right| $ is

The value of the determinant $\left| \begin{array}{ccc} 4 & -6 & 1 \\ -1 & -1 & 1 \\ -4 & 11 & -1 \end{array} \right|$ is

If the following three linear equations have a non-trivial solution, then
$x+4ay+az=0$
$x+3by+bz=0$
$x+2cy+cz=0$

If $\left|\begin{array}{ccc}2 & 2k & 1 \\ 1 & k-1 & 1 \\ 2 & 1 & k+1\end{array}\right|=Ak^2+Bk+C$, then $A+B+C=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module