​$$\text{The value of } \sqrt{\frac{1 - \cos 300^\circ}{2}} \text{ is:}$$​​

Correct option is A

Given:

​$$\quad \sqrt{\frac{1 - \cos 300^\circ}{2}}$$​​

Concept Used:

​$$cos (2\pi-\theta)=cos\theta$$​​

Solution:

​$$cos300° = cos(360°- 60°) = cos 60°$$ 

we know that cos60° = $$\frac{1}{2}$$ So 

​$$cos 300° = \frac{1}{2}$$​​

Now substitute $$cos300° = \frac{1}{2}$$​ into the given expression:

​$$\sqrt\frac{1 - \cos 300^\circ}{2} = \sqrt\frac{1 - \frac{1}{2}}{2}$$ 

​$$\Rightarrow \sqrt\frac{\frac{1}{2}}{2} = \sqrt\frac{1}{4}$$  

​$$= \frac{1}{2}$$​​

Thus the value of the expression is $$\frac{1}{2}$$ .