State whether the following are true or false. Justify your answer.
The value of $\sin \theta$ increases as $\theta$ increases.
The value of $\sin \theta$ increases as $\theta$ increases in the interval of $0^{\circ}<\theta<90^{\circ}$ as
$\sin 0^{\circ}=0$
$\sin 30^{\circ}=\frac{1}{2}=0.5$
$\sin 45^{\circ}=\frac{1}{\sqrt{2}}=0.707$
$\sin 60^{\circ}=\frac{\sqrt{3}}{2}=0.866$
$\sin 90^{\circ}=1$
Hence, the given statement is true.
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.
Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
If $3 \cot A=4,$ check whether $\frac{1-\tan ^{2} A}{1+\tan ^{2} A}=\cos ^{2} A-\sin ^{2} A$ or not.