#### The value of 2sinθ can be a+1/a , where a is a positive number, and a ≠ 1.

Solution.    We know that
-1≤ sin θ ≤ 1
Multiply by 2.
-2≤ 2 sin θ ≤ 2
Here we found that value of 2 sin $\theta$ is lies from – 2 to 2.
But if we take a > 0 and a $\neq$ 1 then
$a+\frac{1}{a}> 2$
For example a = 3
3 + 1/3 = 3.33
Hence $a+\frac{1}{a}$ is always greater than 2 in case of positive number except 1
But value of 2 sin $\theta$  is not greater than 2
Hence the given statement is false