If theta in left(0, frac{pi}{2}right),then le | vedclass

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

Question

(C) Let the given determinant be $\Delta$. We know that $(a+b)^2 - (a-b)^2 = 4ab$. Applying the operation $C_1 \rightarrow C_1 - C_2$,the first column

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Let the given determinant be $\Delta$. We know that $(a+b)^2 - (a-b)^2 = 4ab$. Applying the operation $C_1 ightarrow C_1 - C_2$,the first column becomes: $C_1(1) = (\sin 	heta + \operatorname{cosec} 	heta)^2 - (\sin 	heta - \operatorname{cosec} 	heta)^2 = 4(\sin 	heta)(\operatorname{cosec} 	heta) = 4(1) = 4$. $C_1(2) = (\cos 	heta + \sec 	heta)^2 - (\cos 	heta - \sec 	heta)^2 = 4(\cos 	heta)(\sec 	heta) = 4(1) = 4$. $C_1(3) = (	an 	heta + \cot 	heta)^2 - (	an 	heta - \cot 	heta)^2 = 4(	an 	heta)(\cot 	heta) = 4(1) = 4$. Now,the determinant is $\Delta = \left|\begin{array}{ccc} 4 & (\sin 	heta-\operatorname{cosec} 	heta)^2 & 2020 \ 4 & (\cos 	heta-\sec 	heta)^2 & 2020 \ 4 & (	an 	heta-\cot 	heta)^2 & 2020 \end{array}ight|$. Since the first column $C_1$ and the third column $C_3$ are proportional (specifically,$C_3 = 505 	imes C_1$),the value of the determinant is $0$.

Similar Questions

$\left| \begin{array}{ccc} a - b & b - c & c - a \\ x - y & y - z & z - x \\ p - q & q - r & r - p \end{array} \right| = $

If $1, \omega, \omega^2$ are the cube roots of unity,then $\Delta = \begin{vmatrix} 1 & \omega^n & \omega^{2n} \\ \omega^n & \omega^{2n} & 1 \\ \omega^{2n} & 1 & \omega^n \end{vmatrix}$ is equal to

Using properties of determinants,prove that:
$\left|\begin{array}{ccc}1 & 1+p & 1+p+q \\ 2 & 3+2 p & 4+3 p+2 q \\ 3 & 6+3 p & 10+6 p+3 q\end{array}\right|=1$

If $D = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}$ and $D' = \begin{vmatrix} a_1 + pb_1 & b_1 + qc_1 & c_1 + ra_1 \\ a_2 + pb_2 & b_2 + qc_2 & c_2 + ra_2 \\ a_3 + pb_3 & b_3 + qc_3 & c_3 + ra_3 \end{vmatrix}$,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module