Evaluate:
$\cos 48^{\circ}-\sin 42^{\circ}$
$0$
$1$
$-1$
$0.5$
$\cos 48^{\circ}-\sin 42^{\circ}=\cos \left(90^{\circ}-42^{\circ}\right)-\sin 42^{\circ}$
$=\sin 42^{\circ}-\sin 42^{\circ}$
$=0$
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 $B$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\frac{1+\sec A}{\sec A}=\frac{\sin ^{2} A}{1-\cos A}$
If $\sec 4 A =\operatorname{cosec}\left( A -20^{\circ}\right),$ where $4 A$ is an acute angle, find the value of $A$. (in $^{\circ}$)
State whether the following are true or false. Justify your answer.
The value of $\cos \theta$ increases as $\theta$ increases
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