The equation cos−1α−θα−β=sin−1θ−βα−β is valid for
α > β and θ takes any value
α = θ = β
α > θ > β or α < θ < β
none of these.
The given equation is valid if α−θα−β>0 and θ−βα−β>0
⇒ Either α>θ>β or α<θ<β