State True or False for the statements. \( \mathrm{P} \) The determ...

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State True or False for the statements.
\( \mathrm{P} \)
The determinant \( \left|\begin{array}{ccc}\sin A & \cos A & \sin A+\cos B \\ \sin B & \cos A & \sin B+\cos B \\ \sin C & \cos A & \sin C+\cos B\end{array}\right| \) is equal to zero.
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