State whether the following is true or false. Justify your answer.
$\cot A$ is not defined for $A = 0^{\circ}$.
$\cot A$ is not defined for $A = 0^{\circ}$.
(TRUE) The statement is true.
We know that $\cot A = \frac{\cos A}{\sin A}$.
For $A = 0^{\circ}$,we have $\cot 0^{\circ} = \frac{\cos 0^{\circ}}{\sin 0^{\circ}}$.
Since $\cos 0^{\circ} = 1$ and $\sin 0^{\circ} = 0$,we get $\cot 0^{\circ} = \frac{1}{0}$.
Division by zero is undefined in mathematics. Therefore,$\cot 0^{\circ}$ is not defined.
We know that $\cot A = \frac{\cos A}{\sin A}$.
For $A = 0^{\circ}$,we have $\cot 0^{\circ} = \frac{\cos 0^{\circ}}{\sin 0^{\circ}}$.
Since $\cos 0^{\circ} = 1$ and $\sin 0^{\circ} = 0$,we get $\cot 0^{\circ} = \frac{1}{0}$.
Division by zero is undefined in mathematics. Therefore,$\cot 0^{\circ}$ is not defined.
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