Explanation

tan θ = sin θ/cos θ and cot θ = cos θ/sin θ

tan θ + cot θ = sin θ/cos θ + cot θ = cos θ/sin θ

= sin^2 θ + cos^2 θ/sin θ cos θ

= 1/sin θ cos θ (since sin² θ + cos² θ = 1)

Now, 1/sin θ cos θ = 1/sin θ × 1/cos θ = cosec θ × sec θ = sec θ cosec θ

The answer is sec θ cosec θ.