Evaluate:

$\cos 48^{\circ}-\sin 42^{\circ}$

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 $\theta$.

If $\sin A =\frac{3}{4},$ calculate $\cos A$ and $\tan A$.

$(1+\tan \theta+\sec \theta)(1+\cot \theta-\operatorname{cosec} \theta)=..........$

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

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

Express $\cot 85^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$