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AP EAMCET20224 Jul 2022Evening ShiftMathematicsTrigonometric EquationsActual

If A + B + C = π , cos B = cos A cos C , then tan A tan C =

Options

  1. A0
  2. B1
  3. C2
  4. D1 2

Correct answer

C. 2

Step-by-step solution

Given, A + B + C = π Now, cos B = cos A cos C ⇒ cos π - A + C = cos A cos C ⇒ - cos A + C = cos A cos C ⇒ cos A cos C - sin A sin C = - cos A cos C ⇒ sin A sin C = 2 cos A cos C ⇒ tan A tan C = 2 .

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