### If tan θ + cot θ = 5, find the value of tan2 θ + cot2 θ.

23

Step by Step Explanation:
1. tan θ + cot θ = 5
2. On squaring both sides,
(tan θ + cot θ)2 = 52
3. tan2θ + cot2θ + 2 tanθ cotθ = 25
4. tan2θ + cot2θ + 2 = 25
5. tan2θ + cot2θ = 25 - 2 = 23