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


Answer:

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

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