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      Question

      If tan θ + cot θ = 16, then find the value of

      tan2θ + cot2θ.
      A 324 Correct Answer Incorrect Answer
      B 254 Correct Answer Incorrect Answer
      C 258 Correct Answer Incorrect Answer
      D 196 Correct Answer Incorrect Answer

      Solution

      We know that, (a + b) 2 = a2 + b2 + 2ab

      So, (tan θ + cot θ) 2 = tan2 θ + cot2 θ + 2 x tan θ x cot θ

      So, 162 = tan2 θ + cot2 θ + (2 x 1)

      So, tan2 θ + cot2 θ = 256 - 2 = 254

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