Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to n times the magnitude of A - B, then the angle between A and B is

Let $\theta$ be the angle between A and B,

$|\mathrm{A}+\mathrm{B}|=n| \mathrm{A}-\mathrm{B}|$ 

$\Rightarrow \sqrt{A^2+B^2+2AB\cos \theta }$

$=n\sqrt{A^2+B^2+2AB\cos \left(180°-\theta \right)}$ 

$2x^2(1+\cos \theta )=n^2·2x^2(1-\cos \theta )$

$1+\cos \theta =n^2-n^2\cos \theta$

$\left(1+n^2\right)\cos \theta =n^2-1$ 

$\cos \theta =\frac{n^2-1}{n^2+1}$

$\theta ={\cos }^{-1}\left(\frac{n^2-1}{n^2+1}\right)$