JEE Physics Practice Question

Two vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ have equal magnitudes. The magnitude of $$\left( {\overrightarrow A + \overrightarrow B } \right)$$ is 'n' times the magnitude of $$\left( {\overrightarrow A - \overrightarrow B } \right)$$ . The angle between $${\overrightarrow A }$$ and $${\overrightarrow B }$$ is -

1. A.$${\sin ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$
2. B.$${\sin ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$
3. C.$${\cos ^{ - 1}}\left[ {{{{n^2} - 1} \over {{n^2} + 1}}} \right]$$
4. D.$${\cos ^{ - 1}}\left[ {{{n - 1} \over {n + 1}}} \right]$$