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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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