Evaluate left|begin{array}{cc}cos 15^{circ} | vedclass

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

Question

(B) To evaluate the determinant $\left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \ \sin 75^{\circ} & \cos 75^{\circ}\end{array}ight|$,we u

Vedclass · Accepted Answer

$ 0 $

Vedclass · Answer

(B) To evaluate the determinant $\left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \ \sin 75^{\circ} & \cos 75^{\circ}\end{array}ight|$,we use the formula for a $2 	imes 2$ determinant: $\left|\begin{array}{cc}a & b \ c & d\end{array}ight| = ad - bc$.Applying this to the given matrix:$\cos 15^{\circ} \cos 75^{\circ} - \sin 15^{\circ} \sin 75^{\circ}$Using the trigonometric identity $\cos(A + B) = \cos A \cos B - \sin A \sin B$,where $A = 15^{\circ}$ and $B = 75^{\circ}$:$\cos(15^{\circ} + 75^{\circ}) = \cos(90^{\circ})$Since $\cos(90^{\circ}) = 0$,the value of the determinant is $0$.

Evaluate $ \left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right| $

Similar Questions

Let $\omega = -\frac{1}{2} + i \frac{\sqrt{3}}{2}$,where $i = \sqrt{-1}$. Then the value of $\left| \begin{array}{ccc} 1 & 1 & 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega^4 \end{array} \right|$ is

If $\left| \begin{array}{ccc} 1 & 2 & 3 \\ 2 & x & 3 \\ 3 & 4 & 5 \end{array} \right| = 0$,then $x =$

If ${\Delta _1} = \left| {\begin{array}{{20}{c}}1&0\\a&b\end{array}} \right|$ and ${\Delta _2} = \left| {\begin{array}{{20}{c}}1&0\\c&d\end{array}} \right|$,then ${\Delta _2}{\Delta _1}$ is equal to

Let $A = \begin{bmatrix} 3-t & 1 & 0 \\ -1 & 3-t & 1 \\ 0 & -1 & 0 \end{bmatrix}$ and $\det(A) = 5$, then find the value of $t$.

The value of the determinant $\left| \begin{array}{ccc} 10! & 11! & 12! \\ 11! & 12! & 13! \\ 12! & 13! & 14! \end{array} \right|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module