If α,β are positive acute angles and cos2α=3cos2β−13−cos2β, then tanα=ktanβ such that
cos(2α)=3cos2β−13−cos2β
Or
1−cos2α1+cos2α=(3−cos2β)−(3cos2β−1)(3−cos2β)+(3cos2β−1)
Or
tan2α=4(1−cos2α)2(1+cos2α)
Or
tan2α=2tan2β
Or
tanα=√2tanβ. since 0<α,β<900.