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      Question

      If  tan 12θ x tan 6θ = 1 then the value of tan 9θ

      is
      A √3 Correct Answer Incorrect Answer
      B 1 Correct Answer Incorrect Answer
      C ∞ Correct Answer Incorrect Answer
      D 1/√3 Correct Answer Incorrect Answer

      Solution

      We know that ,If tanA ` ` tanB = 1 then A & B are complementary angles it means  A + B = 90˚ As it is given by tan 12θ . tan 6θ = 1 so 12θ+6θ = 90˚ or 18θ = 90˚ So θ = 5˚ Hence tan 9θ = tan (9 x 5˚) = tan 45˚ = 1

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