The value of


The value of $2 \sin \theta$ can be $a+\frac{1}{a}$ where $a$ is a positive number and $a \neq 1$.



Given, $a$ is a positive number and $a \neq 1$, then $A M>G M$

$\Rightarrow \quad \frac{a+\frac{1}{a}}{2}>\sqrt{a \cdot \frac{1}{a}} \Rightarrow\left(a+\frac{1}{a}\right)>2$

[since, $\mathrm{AM}$ and $\mathrm{GM}$ of two number's $\mathrm{a}$ and $\mathrm{b}$ are $\frac{(a+b)}{2}$ and $\sqrt{a b}$, respectively]

$\Rightarrow \quad 2 \sin \theta>2$ $\left[\because 2 \sin \theta=a+\frac{1}{a}\right]$

$\Rightarrow \quad \quad \sin \theta>1$ $[\because-1 \leq \sin \theta \leq 1]$

Which is not possible.

Hence,the value of $2 \sin \theta$ can not be $a+\frac{1}{a}$

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