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 $a \neq 1$.

(B) False.
Given that $a$ is a positive number and $a \neq 1,$ we apply the Arithmetic Mean-Geometric Mean $(AM-GM)$ inequality.
For any two positive numbers $a$ and $\frac{1}{a},$ the $AM$ is $\frac{a + \frac{1}{a}}{2}$ and the $GM$ is $\sqrt{a \cdot \frac{1}{a}} = 1.$
Since $AM > GM$ for $a \neq 1,$ we have $\frac{a + \frac{1}{a}}{2} > 1,$ which implies $(a + \frac{1}{a}) > 2.$
If we assume $2 \sin \theta = a + \frac{1}{a},$ then $2 \sin \theta > 2,$ which means $\sin \theta > 1.$
However,we know that the range of $\sin \theta$ is $[-1, 1],$ so $\sin \theta$ can never be greater than $1.$
Therefore,the statement is False.