If $\operatorname{cosec} A = \sqrt{10}$,then $\sin A = \dots$

Which of the following is true for some $\theta$ (where,$0 < \theta < 90^{\circ}$)?

In $\triangle ABC$,right-angled at $B$,$AB = 24 \, cm$,$BC = 7 \, cm$. Determine:
$(i)$ $\sin A, \cos A$
$(ii)$ $\sin C, \cos C$

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

If $5 \theta$ is the measure of an acute angle and $\cos \theta = \sin 5 \theta$,then the value of $\theta$ is $\ldots \ldots \ldots \ldots$ (in $^{\circ}$)

Write 'True' or 'False' and justify your answer.
The value of $2 \sin \theta$ can be $(a + \frac{1}{a}),$ where $a$ is a positive number,and $a \neq 1$.