Explanation

Combining the fractions: cosθ/(1−sinθ)+cosθ/(1+sinθ)=2cosθ/cos²θ=2secθ=4, so secθ=2 and tanθ=√3. Then tan²θ+cot²θ=3+1/3=10/3, option B. A sign error when combining the two denominators leads to 2cosθ/sin²θ and one of the wrong options.