Which of the following relations is true for two unit vectors $\hat{ A }$ and $\hat{ B }$ making an angle $\theta$ to each other$?$
$|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \tan \frac{\theta}{2}$
$|\hat{ A }-\hat{ B }|=|\hat{ A }+\hat{ B }| \tan \frac{\theta}{2}$
$|\hat{ A }+\hat{ B }|=|\hat{ A }-\hat{ B }| \cos \frac{\theta}{2}$
$|\overrightarrow{ A }-\hat{ B }|=|\overrightarrow{ A }+\hat{ B }| \cos \frac{\theta}{2}$
Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$
$(A)$ It is possible to have $| \overrightarrow C | < | \overrightarrow A |$ and $ | \overrightarrow C | < | \overrightarrow B|$
$(B)$ $|\overrightarrow C |$ is always greater than $|\overrightarrow A |$
$(C)$ $|\overrightarrow C |$ may be equal to $|\overrightarrow A | + |\overrightarrow B|$
$(D)$ $|\overrightarrow C |$ is never equal to $|\overrightarrow A | + |\overrightarrow B|$
Which of the above is correct
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