Two vectors → P and → Q have equal magnitudes. If the magnitude of...

$| \overset{\to}{P} | = | \overset{\to}{Q} | = x \ldots \left(i\right)$

$| \overset{\to}{P} + \overset{\to}{Q} | = n | \overset{\to}{P} - \overset{\to}{Q} |$

${P}^{2} + {Q}^{2} + 2PQcos\theta = {n}^{2}\left({P}^{2} + {Q}^{2} - 2PQcos\theta\right)$

Using$( i )$ in above equation,

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

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