Given: ∣A+B∣=n∣A−B∣, so, the magnitudes of this will be given as,
A2+B2+2ABcosθ=n(A2+B2−2ABcosθ);where θ is the angle between A and B.
Also, ∣A∣=∣B∣,
2A2+2A2cosθ=n2A2−2A2cosθ
Squaring both sides:
2A2(1+cosθ)=n22A2(1−cosθ)
cosθ=n2+1n2−1
i.e., θ=cos−1[n2+1n2−1]