Concept:The range of x+x1 for real x does not intersect the range of cosθ.Explanation:Let f(x)=x+x1, with x=0.For x>0, by AM–GM, x+x1≥2, with equality at x=1.For x<0, set y=−x>0. Then x+x1=−(y+y1)≤−2, with equality at y=1 (x=−1).Thus, f(x)∈(−∞,−2]∪[2,∞).For a real angle θ, cosθ∈[−1,1].The intervals [−1,1] and (−∞,−2]∪[2,∞) have no common values.Hence, no real θ can satisfy cosθ=x+x1.Answer:Option B: No value of θ is possible.