$\sin 2 A=2 \sin A$ is true when $A=$

State whether the following are true or false. Justify your answer.

$\cot$ $A$ is not defined for $A =0^{\circ}$

Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.

State whether the following are true or false. Justify your answer.

The value of $\sin \theta$ increases as $\theta$ increases.

If $\tan 2 A=\cot \left(A-18^{\circ}\right),$ where $2 A$ is an acute angle, find the value of $A .$ (in $^{\circ}$)

State whether the following are true or false. Justify your answer.

$(i)$ $\cos A$ is the abbreviation used for the cosecant of angle $A$

$(ii)$ cot $A$ is the product of cot and $A$.

$(iii)$ $\sin \theta=\frac{4}{3}$ for some angle $\theta$.