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

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(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

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$ 0 $

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(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| $

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