left|begin{array}{rr}sin 35^{circ} & -cos 35^ | vedclass

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(C) To evaluate the determinant $\left|\begin{array}{rr}\sin 35^{\circ} & -\cos 35^{\circ} \ \sin 55^{\circ} & \cos 55^{\circ}\end{array}ight|$,we

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$1$

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(C) To evaluate the determinant $\left|\begin{array}{rr}\sin 35^{\circ} & -\cos 35^{\circ} \ \sin 55^{\circ} & \cos 55^{\circ}\end{array}ight|$,we use the formula for a $2 	imes 2$ determinant: $\left|\begin{array}{rr}a & b \ c & d\end{array}ight| = ad - bc$.Applying this to the given matrix:$= (\sin 35^{\circ})(\cos 55^{\circ}) - (-\cos 35^{\circ})(\sin 55^{\circ})$$= \sin 35^{\circ} \cos 55^{\circ} + \cos 35^{\circ} \sin 55^{\circ}$Using the trigonometric identity $\sin(A + B) = \sin A \cos B + \cos A \sin B$,where $A = 35^{\circ}$ and $B = 55^{\circ}$:$= \sin(35^{\circ} + 55^{\circ})$$= \sin(90^{\circ})$$= 1$Thus,the correct option is $C$.

$\left|\begin{array}{rr}\sin 35^{\circ} & -\cos 35^{\circ} \\ \sin 55^{\circ} & \cos 55^{\circ}\end{array}\right|=$ . . . . . .

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