Question

Question 9
The value of $2sin\theta$ can be $a+\frac{1}{a}$, where a is a positive number and $a\ne 1$.

Answer 1

The statement is false.

Given, a is a positive number and $a\ne 1$, then AM > GM.

$\Rightarrow \frac{a+\frac{1}{a}}{2}>\sqrt{a.\frac{1}{a}}\Rightarrow (a+\frac{1}{a})>2$

[since, AM and GM of two numbers a and b are $\frac{(a+b)}{2}$ and $\sqrt{ab}$, respectively]

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

$\Rightarrow sin\theta >1[\because -1\le sin\theta \le 1]$

Which is not possible.

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