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 $\tan A =\cot B ,$ prove that $A + B =90^{\circ}$
If $\tan ( A + B )=\sqrt{3}$ and $\tan ( A - B )=\frac{1}{\sqrt{3}} ; 0^{\circ}< A + B \leq 90^{\circ} ; A > B ,$ find $A$ and $B$
$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
If $\sin 3 A =\cos \left( A -26^{\circ}\right),$ where $3 A$ is an acute angle, find the value of $A= . . . . ^{\circ}$.