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      Question

      If tan A = 1 and tan B = √ 3, what is the value of cos

      A . cos B - sin A . sin B?
      A (1 + √3)/2√2 Correct Answer Incorrect Answer
      B (1 - √3)/2√2 Correct Answer Incorrect Answer
      C 2√2/3 Correct Answer Incorrect Answer
      D 1 Correct Answer Incorrect Answer

      Solution

      Given, tan A = 1 β‡’ A = 45Β° Also given, tan B = √ 3 β‡’ B = 60Β° ∴ cos A . cos B - sin A . sin B = cos 45Β° . cos 60Β° - sin 45Β° . sin 60Β° = 1/ √ 2 * 1/2 - 1/ √ 2 . √ 3/2 = (1 - √ 3)/2 √ 2

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