If $\sin \theta = \frac{3}{5}$,then $\tan \theta = \ldots$

The value of the expression $\left[\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right]$ is:

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 $a \neq 1$.

$\cos (40^{\circ}-\theta)-\sin (50^{\circ}+\theta) = \ldots \ldots \ldots \ldots$

If $1+\sin ^{2} \theta=3 \sin \theta \cos \theta,$ then prove that $\tan \theta=1$ or $\frac{1}{2}$.

Write 'True' or 'False' and justify your answer.
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1$